text:
Domains @iitg.ac.in
Varying-order NURBS discretization: An accurate and efficient method for isogeometric analysis of large deformation contact problems
Vishal Agrawal Sachin S. Gautam111Corresponding author, email: ssg@iitg.ac.in
In this paper, a novel varying order NURBS discretization method is proposed to enhance the performance of isogeometric analysis within the framework of computational contact mechanics. The method makes use of higher-order NURBS for contact integral evaluations. Lower-orders NURBS capable of modelling complex geometries exactly are utilized for the bulk discretization. This unexplored idea provides the possibility to refine the geometry through controllable order elevation strategy for isogeometric analysis. To achieve this, a higher-order NURBS layer is used as the contact boundary layer of the bodies. The NURBS layer is constructed using the surface refinement strategies such that it is accompanied by a large number of additional degrees of freedom and matches with the bulk parametrization.
The validity of the presented isogeometric mortar contact formulation with varying-order NURBS discretization is first examined through the contact patch test. The capabilities and benefits of the proposed methodology are then demonstrated in detail using two-dimensional frictionless and frictional contact problems, considering both small and large deformations. It is shown that using the proposed method, accurate solutions can be achieved even with a coarse mesh. It is also shown that the current method requires a considerably lower computational cost compared to standard NURBS discretization while retaining robustness and stability. The simplicity of the method lends itself to be conveniently embedded in an existing isogeometric contact code after only a few minor modifications.
Keywords: Computational contact mechanics; Isogeometric analysis; NURBS; Mortar method; Patch test; Frictional contact.
\AtEveryBibitem\clearfield
isbn \clearfieldissn \clearfieldmonth \renewbibmacrovolume+number+eid\printfieldvolume\setunit \printfieldnumber\setunit \printfieldeid \DeclareFieldFormat[article]number\mkbibparens#1 \DeclareFieldFormat[article]volume\mkbibbold#1 ††affiliationtext: Department of Mechanical Engineering,
Indian Institute of Technology Guwahati, Guwahati, Assam, India, 781039
In the last two decades, NURBS-based isogeometric analysis (IGA) [hughes2005] has been established as an advantageous computational technology for various classes of problems, especially to those where the geometric approximation adversely influence the accuracy of the solution. This is attributed to the distinguished intrinsic features of its underlying basis function, viz. the ability to represent complex geometry exactly even with a coarse mesh, variational diminishing and convex-hull properties, tailorable inter-element continuity, and non-negativeness [hughes2005, Cottrell2009] . Contact modelling belongs to one of these classes that has particularly been benefited from the aforementioned features of the IGA technology. Higher-order smoothness of the NURBS discretized geometry directly provides the continuous normal vector field across the boundary of the contact elements. Thus, eliminates the need of additional contact surface smoothening approaches [Padmanabhan2001, El-Abbasi2001, Wriggers2001, Krstulovi2002, Al-Dojayli2002, Stadler2003] often utilized in the context of finite element method.
The first investigations on the treatment of contact problems using isogeometric analysis are conducted by Temizer et al. [Temizer2011, Temizer2012] , Lu [Lu2011] , and De Lorenzis et al. [DeLorenzis2011, DeLorenzis2012] .
Temizer et al. [Temizer2011] applied the isogeometric analysis to three-dimensional thermomechnical frictionless contact using the mortar contact formulation. They demonstrated that NURBS based discretization achieves superior results in terms of quality and robustness over its counterpart Lagrange discretization. Their investigation of the classical Hertz contact problem showed that the stress oscillation error near the boundary of the contact zone reduces with increasing the order of NURBS interpolations. However, a very fine mesh is still required to get the result which closely matches with the exact solution. Moreover, the non-mortar contact formulation is found to be over-constrained in nature and leads to inaccurate results. Lu [Lu2011] combined the isogeometric analysis with the segment-to-segment contact formulation presented by Papadopoulos and Taylor [Papadopoulos1992] . He showed that intrinsically smooth NURBS discretized geometry alleviates the non-physical oscillations of the contact forces and is capable of accurately describing the intricate mechanics of smooth materials such as fabrics. De Lorenzis et al. [DeLorenzis2011] introduced a mortar-based contact formulation in the context of IGA for the investigation of two-dimensional large deformation contact with Coulomb friction. They demonstrated that the magnitude of the non-physical oscillations of the normal and tangential contact reaction forces reduce on increasing the order of NURBS interpolations. They also showed that the oscillation error in the Hertzian contact stress at the boundary of the contact region is reduced if a very fine mesh is used. Moreover, the distributions of the contact responses obtained with the Lagrange based discretizations are found to be highly sensitive to the interpolation order. Later, De Lorenzis et al. [DeLorenzis2012] applied IGA to three-dimensional large deformation frictionless contact with the mortar method. The contact constraints are enforced using the augmented-Lagrangian approach [ALART1991] . Temizer et al. [Temizer2012] introduced a three-dimensional mortar-based frictional contact formulation as an extension of works in [Temizer2011, DeLorenzis2011] . Again, it is shown that increasing the order of the NURBS interpolations improves the smoothness of contact reaction forces. A point-to-segment contact formulation for two-dimensional frictionless contact is presented by Matzen et al. [Matzen2013] , and recently extended to a weighted point-based contact approach for three-dimensional contact [Matzen2016] , both with the IGA. Many researchers have extensively studied the application of mortar method in the context of IGA [Kim2012, Temzier2013Multiscale, Dittmann2014, BRIVADIS2015, SEITZ2016, Duong2018] , e.g. Brivadis et al. [BRIVADIS2015] investigated the isogeometric mortar method from the theoretical as well as the numerical point of view. Seitz et al. [SEITZ2016] developed a dual mortar method for isogeometric contact analysis. Recently, Duong et al. [Duong2018] introduced a segmentation-free isogeometric mortar contact formulation. A number of works have explored the application of collocation methods to different contact problem using IGA, e.g. [KRUSE2015, DELORENZIS2015, Weeger2018] . De Lorenzis et al. [DeLorenzis2014] presented a detailed review of various isogeometric based treatment procedures for contact problems.
From the above-reviewed literature on contact modelling using IGA, it is evident that NURBS-based discretization delivers significantly superior performance in terms of accuracy, stability, and robustness compared to Lagrange discretization. However, the application of existing NURBS-based discretization approach to isogeometric contact analysis is computationally expensive since due to the rigid tensor nature of the NURBS structures the mesh can only be refined in a global manner. Moreover, the interpolation order of NURBS functions employed for the discretization of the contact boundary layer and for the remaining bulk domain of the geometry has to be uniformly elevated. From the analysis point of view, this may not be desirable since the accuracy of the contact solution is primarily governed by the description of the contact interface. According to literature, to enable the local mesh refinement in the context of isogeometric contact, T-splines [BAZILEVS2010Tspline, DORFEL2010, Scott2011, Dimitri2014Tspline, Dimitri2014, Dimitri2017] , NURBS-based hierarchical refinement [Temizer20161, Temizer20162] , and locally refined (LR) NURBS [Sauer2017] approaches have been adopted. T-splines have been utilized for studying cohesive/contact interface debonding [Dimitri2014Tspline, Dimitri2014, Dimitri2017] . Temizer and Hesch [Temizer20162] , and Hesch et al. [Temizer20161] used the hierarchical NURBS for the treatment of frictionless and frictional contact, respectively. Zimmermann and Sauer [Sauer2017] introduced LR NURBS for the analysis of contact computations of solids and membranes. However, the idea to refine the geometry through controllable order elevation strategy remains unexplored as already noted by Temizer et al. [Temizer2012] .
In the context of finite element contact analysis, to avoid the usage of higher-order NURBS for the bulk description, considerable research progress has been made that combines the intrinsic features of NURBS with the FE discretization [Corbett2014, Corbett2015, RASOOL2016182, MALEKIJEBELI2018, Otto2018, DIAS2019] . Corbett and Sauer [Corbett2014, Corbett2015] introduced a NURBS-enriched contact element formulation which combines the geometric smoothness of NURBS with the efficiency characteristic of the FE discretization. The potential contact layer of each finite element is locally replaced by a NURBS layer, resulting in "NURBS-enriched contact finite elements." Their work is based on the contact element enrichment strategy of Sauer [Roger2011_enrichment, Sauer2013] , which used higher-order Lagrange and Hermite functions on the contact surface. Later, Maleki-Jebeli et al. [MALEKIJEBELI2018] proposed a hybrid isogeometric-finite element discretization method where the advantages of NURBS are exploited in two-dimensional cohesive interface contact/debonding. The bulk domain is given by FE discretization. The transition from NURBS to FE discretizations is carried out using the so called "transition elements", originally presented in [Corbett2014] . Otto et al. [Otto2018] proposed a coupled FE-NURBS discretization approach where an auxiliary NURBS layer is placed between the contact zone of higher-order FE discretized contacting bodies. In order to tie the NURBS layer with FE discretization the pointwise and mortar mesh tying approaches are used. Recently, Dias et al. [DIAS2019] presented a higher-order mortar-based contact element, where the contact interface and bulk are discretized using the hp−FEM. In contrast to enrichment approach of Corbett and Sauer [Corbett2014, Corbett2015] , they used higher-order Lagrange functions as a basis for the discretization of the contact interface, domain, and approximation of the solution field. NURBS are only used to map the position of FE contact layer nodes.
On the other hand, in the context of isogeometric contact analysis, no such effort has been devoted that directly allows the controllable order elevation [Temizer2012] and accordingly complements the performance of IGA while fully retaining its intrinsic key features.
In the present work, a novel varying-order NURBS discretization method is thus proposed where the user-defined higher-order NURBS interpolations are used for the contact computations. The minimum-order NURBS capable of representing the complex geometries exactly are used for the description of the bulk domain. To achieve this, a higher-order NURBS layer is used as the contact boundary layer of the body. This, as a result, avoids the application of higher-order NURBS in the region away from the contact interface. The layer is constructed using different surface refinement strategies in such a manner that it is accompanied by a large number of additional degrees of freedom and matches the bulk parametrization. The proposed varying order NURBS discretization method is accordingly denoted by Np−Npc, where Np is the order of the NURBS basis utilized for the description of the bulk domain and Npc,(pc>p) is the order of NURBS for the contact boundary layer. In the current work, this methodology is applied to two-dimensional frictionless and frictional contact problems, considering both small and large deformations. Due to its simplicity, the proposed approach can be conveniently embedded into an existing IGA contact code after only a few modifications.
The mortar method, originally introduced as a domain decomposition technique [mortar1990] , ensures the stability of the contact solution and provides optimal convergence rates, see e.g. Fisher and Wriggers [Fischer2005] , Puso and Laursen [PUSO2004] , Tur et al. [TUR2009] , Hesch and Betsch [Hesch2009] , and Popp et al. [POPP2013] . In this work, the mortar isogeometric contact formulation presented by De Lorenzis et al. [DeLorenzis2011] is extended for varying-order NURBS discretization. The impenetrability and sticking constraints are enforced in a weak sense at the active control points. For the regularization of the impenetrability and tangential sticking constraints the penalty method is adopted.
The remainder of the paper is structured as follows. In Section 2, the mortar based contact formulation for the large deformation frictional problem in the continuum setting along with the standard NURBS discretization procedure are presented. The varying-order NURBS discretization method and its implementation into the existing IGA contact code are described in Section 3. In Section 4, three, two-dimensional numerical examples are presented. First example examines the validity of the mortar isogeometric contact formulation with varying-order NURBS discretization using the contact patch test. In the next two examples, the performance of the proposed discretization method is demonstrated using the classical Hertz and large deformation ironing contact problems. Finally, Section 5 concludes the paper with possible future directions.
2 Contact problem description and NURBS discretization
In this section, first, we present the computational formulation for two-dimensional large deformation frictional contact between two deformable bodies [laursen2003, Wriggers2006] . Next, the existing NURBS-based discretization approach used for the continuum and the contact boundary layer is described. The associated issues are also highlighted.
2.1 Computational contact formulation
It is assumed that two hyperelastic bodies, where one of them is denoted as slave, Bs, and other as master, Bm, come into contact and undergo finite deformations.
The current configuration of body Bk, k={s,m}, is given by xk=Xk+uk, where Xk and xk represent the coordinates of a generic point in the reference and current configuration, respectively, and uk is the displacement field.
The master surface Γm is parametrized using the convective coordinate ξm that defines covariant vector τ1=xm,ξm, where the contravariant vector τ1:=m11τ1 and m11:=1/(τ1⋅τ1).
In the current configuration, the contact surface of body Bk is described as Γkc:=Γsc=Γmc (assuming perfect contact). The closest contact point ¯xm∈Γmc corresponding to fixed slave point xs∈Γsc is computed via intersecting the master surface Γmc with a line that passes through xs in the direction of unit normal vector n (where n=nm) with closest point projection procedure [KONYUKHOV2008] . In the present formulation, the contact region is pulled back to the reference configuration of the slave contact surface Γsc0, henceforth, all the contact integrals will be computed on Γsc0. For the unbiased treatment of the contacting bodies, we refer to work by Sauer and De Lorenzis [unbiased2013, unbiased2015] .
The minimum normal gap gN is defined as
gN=(xs−¯xm)⋅¯n,~{}~{}~{}~{}~{}~{}where~{}~{}¯xm=xm(¯ξm). (1)
Here, xs is a point on the slave surface Γsc, ¯xm is the corresponding physical coordinate of the closest contact point on the master surface Γmc and ¯n is the unit normal vector at ¯xm.
The tangential relative gap ˙gT is defined in incremental form as
˙gT=˙¯ξm⋅τ1→(gT−gTn)/Δt=(¯ξm−¯ξmn)/Δt τ1, (2)
which is in agreement to the time-discretized backward Euler formulation. Here, as well in the following, all the contact quantities will be expressed by default to the current time step t=tn+1, while the subscript n is used to define quantities at previous step tn.
The contact traction vector t in the current configuration is defined in terms of its normal and tangential components as
t=tN+tT=tN¯n+tT¯τ1. (3)
In case of gN<0, the normal contact tractions tN=t⋅n are activated that avoid the penetration of the contact regions. In order to enforce the impenetrability in the normal direction, following Karush-Kuhn-Tucker (KKT) conditions must be satisfied [Wriggers2006]
gN≥0, tN≤0, gNtN=0, ˙% gNtN=0, (4)
and the KKT conditions for Coulomb friction law in the tangential direction are [Wriggers2006]
Φ=||tT||−μtN≤0, γ≥0, γΦ=0, (5)
where μ and γ are the Coulomb friction coefficient and tangential slip velocity, respectively.
It is noted that the above-described contact constraints cannot be directly incorporated into the variational form as they lead to the non-smooth relationship between the normal gap and the contact pressure, resulting in a non-smooth normal contact constitutive law. In the present work, the penalty method is adopted for the regularization of the contact constraints defined in Eqs. (4) and (5). The penalty regularized normal contact constraint is defined as
tN=ϵN⟨gN⟩, where ⟨gN⟩={gNif gN% ≤0,0otherwise, (6)
where ϵN>0 denotes the normal penalty parameter. The regularized frictional contact constraints in the tangential direction yields:
tT = tTn+ϵT[m11(¯ξm−¯ξmn)−γtT|tT|],
Φ ≤ 0, γ≥0, γΦ=0, (7)
where ϵT>0 is the tangential penalty parameter. The frictional contact traction is determined based on the classical return-mapping algorithm. The trial tangential traction and contact state are first computed with the assumption that γ=0
ttrialT=tTn+ϵTm11(¯ξm−¯ξmn), Φtrial=||ttrialT||−μtN, (8)
and the status: slip or stick is identified using
tT=⎧⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪⎩ttrial% Tif Φtrial≤0,−μtNttrialT||ttrialT||otherwise\,. (9)
Based on the penalty solution method, the contact contribution to the weak form (contact virtual work) is given by
δWc = ∫Γsc0[tNδgN+tTδ¯ξm] dΓ. (10)
For the evaluation of above contact integral an active set strategy is utilized. The linearization of the contact virtual work δWc, which is necessary for the Newton-Raphson iterative solution method, leads to
ΔδWc=∫Γsc0[Δt% NδgN+tNΔδgN+ΔtTδ¯ξm+tTΔδ¯ξm] dΓ. (11)
Further details, together with the variation and linearization of all quantities such as δgN,ΔgN, ΔδgN, δ¯ξm, Δδ¯ξm, etc., can be found in [DeLorenzis2011, Wriggers2006] .
2.2 NURBS-based discretization
In this subsection, the existing NURBS-based discretizing procedure used for the continuum and the contact surface in the context of IGA is briefly discussed.
The IGA has emerged as a successful integration of computer-aided-design (CAD) and finite element analysis (FEA) [Cottrell2009] . It utilizes the CAD polynomials as a basis for the modelling of complex geometries exactly and the approximation of unknown solution fields. In the present work, NURBS are used for the discretization of the continuum including the contact surface.
NURBS are built from B-splines. For a given knot vector Ξi along the ξi (i=1,2) parametric direction, the B-spline interpolations of order pi are defined using the following Cox-de Boor recursive relation [nurbsbook] :
for pi=0, \quadNl,0(ξi) = {1, if ξil≤ξi<ξil+1,0,otherwise. (13)
for pi>0, \quadNl,pi(ξi) = ξi−ξilξil+pi−ξilNl,pi−1+ (14)
ξil+pi+1−ξiξil+pi+1−ξil+1Nl+1,pi−1,
where Nl,pi(ξi)≥0 and ξil∈IR is the l\scriptsize{th} knot of the knot vector Ξi={ξi1,ξi2,…,ξini+pi+1} which is a set of non-decreasing value of parametric coordinates, i.e. ξil≤ξil+1. Also, ni denotes the total number of control points for pi order of B-spline functions along the ξi parametric direction. A p\scriptsize{th}i order B-spline function offers Cpi−m continuity across each knot ξi, where m is the knot multiplicity. In an open knot vector, the first and last knot entries are repeated by pi+1 times that make the functions interpolatory at the end knots.
NURBS are the projective transformation of B-splines. Thus, NURBS additionally utilize the weight values in their construction. For a given knot vector Ξi, a p\scriptsize{th}i order univariate NURBS function along the ξi parametric direction is defined as [nurbsbook]
Rpil(ξi)=wil∑niA=1wiANA,pi(ξi)Nl,pi(ξi), (15)
where Rpil(ξi)≥0 ∀ξi∈Ξi, and wil>0 is the weight value. For a specified control points vector, Xi={Xil}nil=1, a pthi order NURBS curve along the ξi parametric direction can be constructed using the linear combination of univariate NURBS interpolations and the control point's coordinate vector as
C(ξi)=ni∑l=1Rpil(ξi)Xil. (16)
A bivariate continuum patch is defined by the tensor product of the two univariate NURBS curves defined along the ξ1 and ξ2 parametric directions as
S(ξ1,ξ2)=n1∑l=1n2∑m=1Rp1,p2lm(ξ1,ξ2)Xlm, (17)
where {Xlm}n1,n2l,m=1 is the coordinate vector of the control points net X. Here, Rlm(ξ1,ξ2)>0 is the bivariate NURBS basis function defined as the tensor product of two univariate B-spline basis functions along the ξ1 and ξ2 parametric directions as
Rp1,p2lm(ξ1,ξ2)=wlmW(ξ1,ξ2)Nl,p1(ξ1)Nm,p2(ξ2), (18)
with W(ξ1,ξ2)=∑n1l=1∑n2m=1wlmNl,p1(ξ1)Nm,p2(ξ2) as a normalized weight that is given in terms of weight point wlm and B-spline basis functions. A composition of knot vector with associated control points accompanied by weights constitutes a patch. For in detailed description, we refer to monograph by Pigel and Tiller [nurbsbook] and Cottrell et al. [Cottrell2009] .
In the context of IGA, a NURBS discretized geometry can be refined by means of knot insertion (h−refinement), order elevation (p−refinement), and k−refinement strategies [hughes2005] . Within the knot insertion scheme, an additional knot in the knot vector is inserted. If the inserted knot value is unique, an additional knot-span, consequently an element, without changing the inter-element continuity of the NURBS, is introduced. On the other hand, repetition of knots reduce the smoothness of the NURBS basis functions.
In case of order elevation scheme, the geometry is refined by means of raising the order of the NURBS interpolations. For the elevation of order from pi to pi+t, each knot value is repeated by t times. As a result, the continuity of the NURBS remains unchanged during p−refinement.
The particular order of application of order elevation and knot insertion schemes yields k−refinement [hughes2005] . During k−refinement, first, the inter-element continuity of the NURBS interpolations is increased and then, the additional elements within the given knot vector are introduced. On the other hand, if their application order is reversed, i.e. the knot insertion is performed first before the order elevation scheme [Corbett2014] , the inter-element continuity of the NURBS remains unchanged and knot values are repeated due to order-elevation. This, as a result, yields a large number of control points compared to k−refinement strategy.
Within the existing standard NURBS-based discretization approach, to improve the accuracy of the contact solution with a fixed mesh, the interpolation order of the NURBS discretized structure is uniformly elevated. However, this approach is not computationally favorable since the higher-order NURBS used for the approximation of contact integrals have to be employed for the computation of the vast majority of the bulk region away from the contact surface. It therefore becomes desirable to develop an improved NURBS-based discretization method that provides a possibility to perform controllable order-elevation for a NURBS discretized geometry as already suggested in the paper by Temizer et al. [Temizer2012] . Such a method is proposed in this paper and is described in detail in the next Section.
3 Varying-order NURBS-based discretization
In this section, we introduce the theory for the varying-order NURBS discretization method, followed by the description on its integration into an existing isogeometric contact code.
3.1 Varying-order NURBS
Figure 1: A schematic illustration of the VO NURBS discretization method for a given geometry. (a) Exact representation of the geometry with minimum p1 and p2 order of NURBS along the ξ1 and ξ2 parametric directions with a very coarse mesh. (b) Representation of the VO NURBS discretized geometry where higher-order NURBS (i.e. pc>p1) are used for contact boundary layer and minimum order NURBS interpolations are used for the remaining bulk domain. The accompanied control points are shown with red dots and the new contact boundary layer with bold green line. The corresponding basis functions for the contact surface and bulk domain are also shown.
The basic concept of the varying-order (VO) NURBS discretization for isogeometric contact analysis is illustrated in Fig. 1. Consider a body Bk having contact boundary layer Γkc. Let p1 and p2 be the minimum orders of NURBS basis functions capable of representing the geometry in an exact manner and a coarse mesh is given by the product of open knot vectors Ξ1 × Ξ2 defined along the ξ1 and ξ2 parametric directions as shown in Fig. (a)a. Next, in order to make use of higher-order NURBS interpolation functions for contact computations, the discretized contact boundary Γkc is replaced with a NURBS layer of order pc>p1 as shown in Fig. (b)b.
The NURBS layer is constructed using k−refinement or through a combination of k−refinement and order-elevation [Corbett2014] strategies in such a manner that it matches the bulk parametrization. The application of the k−refinement strategy to the NURBS contact layer increases the order as well as the inter-element continuity of the NURBS basis functions. On the other hand, application of one or two additional steps of order-elevation to k−refined NURBS layer introduces a large number of additional control points along the contact boundary layer while the inter-element continuity, i.e. Cpc−1, remains unchanged. This way, (i) the higher-order NURBS basis functions are utilized for the evaluation of contact contributions, (ii) a large number of additional degrees of freedom are introduced across the contact surface with a fixed mesh, and (iii) the minimum order NURBS are employed for the description of the bulk domain that does not come into contact. The resulting isogeometric contact element is characterized by necp=(pc+1)+(p1+1)×p2 number of control points, where pc+1 on the contact layer and (p1+1)×p2 on the remaining three faces of each element. The bivariate NURBS basis functions for such an element are defined as
Rpc,p21(ξ1,ξ2) := w11W(ξ1,ξ2)N1,pc(ξ1)N1,p2(ξ2),
⋮ ⋮
Rpc,p2pc+1(ξ1,ξ2) := w(pc+1)1W(ξ1,ξ2)Npc+1,pc(ξ1)N1,p2(ξ2), (19)
Rp1,p2pc+2(ξ1,ξ2) := w12W(ξ1,ξ2)N1,p1(ξ1)N2,p2(ξ2),
Rp1,p2necp(ξ1,ξ2) := w(p1+1)2W(ξ1,ξ2)Np1+1,p1(ξ1)N2,p2(ξ2),
where the normalizing weight is given by
W(ξ1,ξ2)=(pc+1)∑i=1wi1Ni,pc(ξ1)N1,p2(ξ2)+(p1+1)∑i=1wi2Ni,p1(ξ1)N2,p2(ξ2). (20)
The basis functions in Eq. (3.1) exhibit the non-negativity property
Rpc,p2A(ξ1,ξ2)≥0 ∀ ξ1,ξ2∈Ω where A=1,2,…,necp, (21)
and they also satisfy the partition of unity property:
necp∑A=1Rpc,p2A(ξ1,ξ2)=1, ∀ ξ1,ξ2∈Ω. (22)
Using the isoparametric concept, the basis functions defined in Eq. (3.1) are employed for the approximation of the unknown displacement ue field, its variation δue, and the current coordinates xe as
ue=necp∑A=1Rpc,p2AuA, δue=necp∑A=1Rpc,p2AδuA, and xe=necp∑A=1Rpc,p2AxA, (23)
where, uA, δuA and xA are the displacement, its variation and the current coordinate vector corresponding to the A\scriptsize{th} control point, respectively.
The proposed VO NURBS based discretization approach generalizes the enrichment strategy of Corbett and Sauer [Corbett2014] , which can be constructed using the current methodology by discretizing the region other than the contact boundary layer with the linear-order NURBS interpolations. Moreover, unlike the enrichment strategy of [Corbett2014] , the current discretization approach does not require Bézier extraction operator [Bezier_extraction_NURBS] , which is required to enable the incorporation of NURBS basis into the finite element code structure.
3.2 Implementation into existing code
For integrating the VO NURBS discretization strategy into the existing isogeometric contact code, only minor modifications are required. First of all, for a given mesh resolution, a pc>p1 order of NURBS curve representing the contact boundary layer of the body Bk is constructed. After that, the parametrization for the initially described p1 order NURBS contact layer is replaced with that of the newly constructed pc order curve. For this, a certain number of conditions are needed to be fulfilled. The total number of control points defining the body must be updated to allow the incorporation of the pc order contact curve. This means that the connectivity array for contact elements must be adapted in a manner that it contains all the underlying control points. The contact element connectivity arrays can have a different length than the bulk element connectivity arrays. The bivariate NURBS basis functions for contact elements are evaluated at the quadrature points according to Eq. (3.1). Within each contact element, (pc+1)×(p2+1) number of Gauss-Legendre quadrature points are employed for the evaluation of the weak form obtained through the NURBS interpolation. This ensures the quadratic convergence-rate during the Newton-Raphson iterations. Optimal quadrature rules [Hughes2010, AURICCHIO2012, FAHRENDORF2018] , which are well-suited for IGA, can also be opted for the reduced numerical evaluation. With the exception of these modifications, no other changes are needed to be made in an existing code. The local quantities, e.g. stiffness matrices and force vector, are assembled to their global part in the same way as with the standard procedure. The reader is referred to Agrawal and Gautam [Agrawal2018] for detailed description on the implementation of IGA in a simplified manner.
4 Numerical Examples
In this section, we show the capabilities and performance of the proposed VO NURBS discretization method over the existing standard NURBS discretization approach using three, two-dimensional small and large deformation contact problems. In the first example, the contact patch test is considered to test the validity of the mortar contact formulation for VO NURBS discretizations. Next, the numerical results and the analytical solution of the Hertz contact problem are compared on the basis of accuracy and overall processing time for VO and standard NURBS discretizations. In the final example, a large deformation frictional ironing problem is solved to demonstrate the superiority of the proposed discretization method over the standard approach in terms of accuracy, efficiency, and robustness.
Figure 2: Contact patch test: problem setup, boundary conditions, and mesh.
4.1 Contact patch test
The first example considers a simplified form of the contact patch test originally proposed by Taylor and Papadopoulos [Taylor1991] . The purpose of this example is to verify whether the assemblage of displacement based isogeometric contact elements for VO NURBS discretization is complete. The contact algorithm that passes the contact patch test ensures the convergence of contact solution upon the mesh refinement. Otherwise, solution errors at the contact interface do not necessarily reduce with decreasing the mesh size [Bathe2001] .
The setup of the patch test, taken from Matzen and Bischoff [Matzen2016] , is illustrated in Fig. 2. In this, two blocks, which are modelled using isotropic linear elastic material with Young's modulus E=100 N/mm2 and Poisson's ratio ν=0.0 under the plane stress condition, are positioned on top of each other. The top line of the upper block is subjected to prescribed vertical displacement uy=−0.2 mm. The bottom line of the lower block is fixed against vertical displacement. For the considered displacement-based loading condition, the contact line is expected to deform uniformly by uy=−0.1 mm.
To deal with the worst case scenario, the non-conforming mesh at the contact interface is considered as shown in Fig. 2. For the bulk, second order (p=2) NURBS are used and the contact boundary is given by pc=3, and 4 order of the NURBS layer. For the purpose of comparison, quadratic order of NURBS discretization, i.e. N2, is employed.
Figure 3: The contour plot of vertical displacement uy for N2−N3 discretization.
Figure 4: The deviation of vertical displacement uy along the contact interface from the exact solution for N2, N2−N3, and N2−N4 discretizations.
Figure 3 shows the contour plot of vertical displacement uy for N2−N3 discretization. It can be observed that a uniform gradient of uy develops between the top and the bottom lines of the setup that ranges from −0.2 to 0.0 mm. The gradient of uy remains constant in the horizontal direction. Identical displacement contour plots have been obtained for N2−N4 and N2 discretizations.
Figure 4 illustrates the deviation of numerically evaluated vertical displacement along the contact interface from the exact solution, i.e. uy=−0.1 mm, for N2, N2−N3, and N2−N4 discretizations. It can be observed that the deviation of vertical displacement from analytical solution reduces on increasing the order of NURBS interpolations for contact boundary from pc=2 to pc=3, and 4. This is due to employing higher order (pc=3, and 4) NURBS for the evaluation of contact integrals, which in turn improves the accuracy of the result compared to N2 discretization with a fixed mesh. It is noted that with standard N3 and N4 discretizations identical to N2−N3 and N2−N4 results are achieved since same order of NURBS functions are used for the contact computations in both the discretization approaches. This supports the proposition that the accuracy of the solution improves on increasing the order of NURBS interpolations for the discretization of the contact surface.
Next, to investigate the convergence behaviour of the mortar contact formulation with VO NURBS discretization, the relative vertical displacement error using the L2−norm with successively refining the coarsest mesh shown in Fig. 2 is reported. Figure 5 shows the convergence plots for N2, N2−N3, and N2−N4 discretizations. It can be observed that the L2−error norm of uy decreases and approaches toward the exact solution as the mesh is refined. The rate of convergence for each case of discretization is one. For a fixed mesh resolution, N2−N4 provides the most accurate result followed by N2−N3 compared to N2 discretization. Quantitatively, the value of relative errors even with the coarsest mesh is below 0.02% for N2−N3 and N2−N4 discretizations, which are probably within the acceptable margins. With the obtained results, it is remarked that the isogeometric mortar contact formulation with VO NURBS is numerically consistent as the obtained result converges to the exact solution with refining the mesh.
Figure 5: Convergence of the vertical displacement uy error norm with mesh refinement for N2, N2−N3, and N2−N4 discretizations.
4.2 Hertz contact problem
Figure 6: Setup for the Hertz problem.
In this example, the frictionless contact of an infinitely long cylinder having outer radius Ro=1 and inner radius Ri=0.1 with a rigid surface is considered. The set-up of the problem, adopted from Temizer et al. [Temizer2011] , is illustrated in Fig. 6. Due to symmetry, only a quarter of the geometry is considered. The cylinder is subjected to the overall force Po=0.001 applied as a distributed vertical load over the top surface of the cylinder. A linearly elastic material with Young's modulus E=1 and Poisson's ration ν=0.3 under the plane strain condition is used for the analysis. The penalty parameter ϵN=104 is chosen as a default value to prevent the penetration of the cylinder into the rigid surface.
Four different mesh arrangements having 72×48, 108×48, 144×48, and 180×48 number of elements along each parametric directions are considered. In order to capture the variation of the contact force along the contact interface, approximately 75% of the total elements in each parametric direction are re-distributed in such a manner that they lie within the 10% surface length of the geometry [Temizer2011] . First, we compare the results for N2−Npc discretizations, where the quadratic order NURBS are used to discretize the bulk domain and pc=3, and 4 order NURBS are used for the contact boundary layer, with that of the standard Np (p=3, and 4) order of NURBS discretizations. Figure 6 illustrates the obtained results for both the discretization approaches with different mesh arrangements. The dimensionless contact pressure ¯p=p/p0 is plotted versus the dimensionless contact coordinate ¯X=x/a, where p is the normal contact pressure evaluated at the active control points and x is the distance of these points from the first point of contact. The analytical solution for the current setup, i.e. the maximum contact pressure p0=0.0264 and the contact area radius a=0.48 are given by the Hertz theory [johnson1987] .
Figure 6: Variation of contact pressure distribution for N2−Npc (pc=3, and 4) and Np (p=3,and 4) discretizations with: (a) 72×48; (b) 72×48; (c) 108×48; (d) 108×48; (e) 144×48; (f) 144×48; (g) 180×48; and (h) 180×48 mesh arrangement.
From Fig. 6, it clear that the contact pressure distributions for N2−Npc (pc=3, and 4) are in excellent agreement with their corresponding standard Np (p=3, and 4) order of NURBS discretizations for the same mesh level. This is due to employing the same order of NURBS interpolations for the evaluation of contact integrals in both the discretization approaches. Further, the accuracy of the contact solution increases monotonically on increasing the mesh resolution and nearly exact result is obtained with a very fine 180×48 mesh arrangement, see Figs. (g)g and (h)h. These results closely match those reported by Temizer et al. [Temizer2011] and Lorenzis et al. [DeLorenzis2011] for the classical Hertz contact problem.
Besides comparing the accuracy of the obtained results for VO NURBS to standard NURBS discretization approach, the associated computational cost in terms of the overall analysis time is also investigated. Figure 7 shows the required time for pre- and post-processing (i/o), contact and contact elements computations, and the bulk element computations for both the discretization approaches. The analysis time associated with each discretization is calculated using
Time percentage=total analysis timemaximum total % analysis time×100, (24)
where the maximum total analysis time is for the standard N4 order of NURBS discretization at the very fine mesh level (180×48) which is the most expensive.
From Figs. (a)a and (b)b, it can be observed that N2−Npc, (pc=3, and 4) utilizes at least 50% lower computational cost than that of corresponding standard discretization with the fixed mesh resolution. It is impressive as N2−Npc (pc=3, and 4) take at most half the computational cost than Np (p=3, and 4) to deliver identical results. The major difference between the overall analysis time for the two discretization methods lies within their bulk element computations. The VO NURBS discretization method employs lower-order NURBS for the bulk description. This, as a result, uses a fewer number of degrees of freedom per element during the bulk element computations compared to corresponding standard Np order of NURBS discretization. The degree of freedom density data for both the discretization approaches with different mesh arrangements is given in Table 1.
Figure 7: Comparative analysis time (in %) for: (a) N2−N3 and N3; and (b) N2−N4 and N4 with different mesh arrangements. The analysis time for N4 discretization with 180×48 mesh is used as a reference.
Discretizations
DOFs
Interface Bulk Total
N2−N3
222 10656 10787
N2−N2⋅1
Table 1: Degrees of freedom density data for both the discretization approaches with different mesh arrangements.
Figure 8: Variation of contact pressure distribution for N2−N2⋅1 and N2−N2⋅2 discretizations with: (a) 72×48; and (b) 72×48 mesh.
Figure 9: Comparative analysis time (in %) for N2−N2⋅1, N2−N2⋅2, N2−N3, N2−N4, and N4 discretizations with different mesh arrangements.
From Figs. (a)a to (f)f, it can be further observed that the distribution of contact pressure curve matches exactly with the analytical solution except at the boundary of contact region. It is affected by the element that lies between the contact and non-contacting region. This is a well known issue for which a number of solution approaches have been introduced, e.g. see [Franke2010, Duong2018] . Within the context of IGA, such oscillation error is alleviated if a very fine mesh is used as shown in Figs. (g)g and (h)h. The present analysis particularly focuses on the use of higher-order NURBS to improve the approximation of the contact pressure at a very coarse mesh. For this, an additional order-elevation refinement scheme over the NURBS discretized contact layer is applied. Performing one and two steps of additional order elevation on N2−N2 results in N2−N2⋅1 and N2−N2⋅2 discretizations, respectively. With this, a large number of additional degrees of freedom across the contact interface are introduced due to the repetition of knots during order elevation. The total numbers of degrees of freedom across the contact interface and in the bulk domain for both the discretizations are also listed in Table 1.
Figure 8 illustrates the results for N2−N2⋅1 and N2−N2⋅2 with 72×48 mesh arrangement. The associated analysis time for these two discretizations are shown in Fig. 9.
From Fig. (b)b, it can be observed that N2−N2⋅2 discretization with 72×48 mesh achieves the accuracy comparable to standard Np (p=3, and 4) order of NURBS discretization based results with a very fine mesh (180×48), see Figs. (g)g and (h)h. This is due to a large number of degrees of freedom present across the contact interface with N2−N2⋅2 which majorly improves the approximation of contact responses with a very coarse mesh. Further, from Fig. 9, it is evident that N2−N2⋅2 takes approximately 90% lower analysis time than that with standard N4 discretization, which is remarkable. The other VO NURBS discretization, e.g. N2−N3⋅2 and N2−N4⋅2, deliver very similar results to N2−N2⋅2. However, they utilize slightly higher computational cost as compared to N2−N2⋅2.
4.3 Frictional ironing problem
The third example considers the ironing problem with two deformable bodies [DeLorenzis2011] . This example is used to demonstrate the performance of VO NURBS discretization in terms of accuracy, robustness, and cost of solution with respect to standard NURBS discretization approach for large deformation and large relative tangential motion with Coulomb friction. The geometric model along with the material details and the boundary condition are shown in Fig. 10. Three nested meshes, which are shown in Fig. 11 and are denoted as m1, m2, and m3, respectively, are used for the die and the slab.
Figure 10: Setup of the ironing problem along with the geometric and material details, and the boundary conditions.
In this example, the die is first pressed downwards into the slab by uniform vertical displacement Uy=−0.2 mm in 10 load steps, and then moved horizontally across the slab by applying a displacement Ux=1.5 mm in 140 load steps. An isotropic, hyperelastic Neo-Hookean material model is considered for both the die and the slab for large deformations. The corresponding constitutive relation is given by [bonet1997]
σ=λJ(lnJ)I+μJ(FFT−I) (25)
where F is the deformation gradient, J=det(F), and I is the identity tensor. In this work, the values for the Lamé constants are defined as λ=2μν/(1−2ν) and μ=E/2(1+ν). The penalty parameters are taken as ϵN=ϵT=100 and the coefficient of sliding friction is μ=0.2. The mortar contact integrals are evaluated using ngp=10 equidistant quadrature points per contact element.
(a) mesh m1
(b) mesh m2
(c) mesh m3
Figure 11: Three different mesh arrangements considered for the die and the slab.
4.3.1 Prediction of contact reaction forces
Figure 12 illustrates the horizontal contact reaction force Px and the vertical contact reaction force Py as a function of load step t for VO N2−Npc (pc=3, and 4) and the standard Np (p=2,3, and 4) order of NURBS discretizations with mesh m1. The results are in agreement with those reported by De Lorenzis et al. [DeLorenzis2011] for the sliding case.
Figure 12: (a) Plot of horizontal and vertical contact reaction forces with load step t. Enlarged view of (b) horizontal contact reaction force Px, and (c) vertical contact reaction force Py for N2−Npc (pc=3, and 4) and standard Np (p=2,3, and 4) discretizations at the coarsest mesh level m1.
The enlarged views for Px and Py are shown in Figs. (b)b and (c)c, respectively. It can be observed that the non-physical oscillations of vertical and horizontal contact reaction forces are present for all the cases during sliding. The oscillation error reduces with increasing the order of NURBS discretization, i.e. from N2 to N4. The curves of Px and Py are indistinguishable for N2−Npc (pc=3, and 4) and standard Np (p=3, and 4) order of NURBS discretizations as expected. This is due to employing the same order of NURBS for the evaluation of contact integrals and identical number of degrees of freedom across the contact boundary in both the cases of discretizations. Table 2 lists degrees of freedom density data for both N2−Npc (pc=3, and 4) and Np (p=3, and 4) order of NURBS discretizations. With N2−N3 and N2−N4, the oscillation amplitude of horizontal contact reaction force ΔPx reduce to approximately 62% and 32%, respectively, of that observed with N2. A quantitative analysis of the reduction in the oscillation error for N2−Npc (pc=3, and 4) and Np (p=2,3, and 4) is given in Table 3 for both the force components. The oscillation amplitude of reaction forces is computed using ΔPj:=max(Pj)−min(Pj), where j=x,y. The associated total computational time for the two discretization approaches is reported in Sec. 4.3.2.
We now present the results for N2−N2⋅1 and N2−N2⋅2 discretizations, where one and two steps of additional order elevation scheme are applied to the N2 discretized contact boundary layer. Figure 13 shows the variation of the horizontal and the vertical contact reaction forces for N2−N2⋅1 and N2−N2⋅2 with respect to most accurate result with the standard N4 order of NURBS. It can be noticed that the oscillation error reduces significantly for the new discretizations. Among the two tested cases, N2−N2⋅2 delivers the best result. It reduces the oscillation amplitude of vertical and horizontal reaction forces to 8.82% and 4.4%, compared to N2. This is attributed to a large number of additional degrees of freedom present across the contact interface when compared to other cases (see Table 2 for degree of freedom details). The other higher-order NURBS layer based discretizations, e.g. N2−N3⋅2 and N2−N4⋅2, also reduce the oscillation error more than N4, although equivalent to N2−N2⋅2 results are obtained as shown in Figs. (b)b and (a)a for N2−N3⋅2 arrangement.
It should be noted that with the most accurate enrichment strategy of Corbett and Sauer [Corbett2014] , i.e. Q1N2.2, the maximum reductions that are achieved in the oscillation amplitude of the horizontal and the vertical contact reaction forces are 11.5% and 11.9%, respectively, of that observed with quadratic NURBS-enriched finite element Q1N2 for the similar sliding case. On comparing the results for N2−N2⋅2 with that of Q1N2.2, it is evident that the VO NURBS based discretization N2−N2⋅2 reduces the oscillation amplitude of horizontal and the vertical contact reaction forces by a factor of approximately 2.16 and 1.35, respectively, of that achieved with Q1N2.2.
DOF for die
DOF for slab
Table 2: Degrees of freedom (DOF) density data for the die and the slab for different VO and standard NURBS discretizations at the mesh level m1.
ΔPx (%)
ΔPy (%)
N2 100 100
N3 60 44.12
N2−N3 62 44.12
N2−N2⋅1 7.1 14.71
N2−N2⋅2 4.4 8.82
Table 3: Reduction in the oscillation amplitude of horizontal and vertical contact reaction forces for different VO and standard NURBS discretizations with the mesh level m1. The oscillation amplitude for N2 is used as a reference.
Such a difference between the performance of N2−N2⋅2 and Q1N2.2 is due to the fact that the accuracy of contact reaction forces does not only depends on the discretization of the contact surface, but also on the bulk deformations as shown in [Corbett2014, Corbett2015] . In contrast to quadratic-order NURBS N2 based mesh, bilinear Lagrange finite elements Q1 based mesh suffers from locking. Thus, N2−N2⋅2 leads to more accurate results than Q1N2.2.
With the obtained results it is clear that the VO NURBS discretization, particularly N2−N2⋅2, is a more effective strategy than the standard NURBS based discretization approach in the context of IGA and the existing enrichment strategy of [Corbett2014] for this case.
Figure 14 shows the contour plot of vertical displacement field uy in the deformed configurations of the setup at different load steps for N2 order of NURBS discretization with mesh m2 arrangement.
Figure 13: Variation of (a) horizontal contact reaction force Px, and (b) vertical contact reaction force Py for different discretizations at the mesh level m1.
Figure 14: Distribution of displacement field uy in the deformed configuration: (a) at the end of the first step (t=10); (b) at step t=80; (c) at the end of second step (t=150), together with the mesh m2 and N2 order of NURBS discretization for the die and the slab.
4.3.2 Computational time
Next, we investigate the reduction in the oscillation amplitude of Px and Py in terms of associated overall computational time upon refining the mesh m1 for the die and slab shown in Fig (a)a. Figure 15 illustrates the results for different VO and standard NURBS discretizations with three meshes m1, m2, and m3. The associated total analysis time for each discretization is calculated using Eq. (24), where the time for N4 order of NURBS at a fine mesh m3 is used as a reference.
From Figs. (a)a and (c)c it is evident that in order to attain the accuracy comparable to N4 discretization, N2−N4 takes at least 40% lower computational time as compared to standard N4 discretization for the same mesh level. Further, from Figs. (b)b and (d)d it is clear that a significant improvement in the accuracy is achieved with N2−N2⋅2 and N2−N3⋅2 for the fixed mesh resolution. It turns out that N2−N2⋅2 with the mesh m1 and m2 yield results comparable to N4 discretizations with the mesh level m2 and m3, respectively. The analysis time for N2−N2⋅2 is still considerably lower, i.e. 40%, than that for N4 discretization. It can also be observed that a good convergence behaviour with VO NURBS is achieved.
Figure 15: Oscillation error of the horizontal contact reaction force Px (top) and the vertical contact force Py (bottom) with overall analysis time (in %) for different VO and standard NURBS discretizations with three different mesh levels (m1, m2, and m3). The total analysis time for standard N4 discretization at the mesh level m3 is used as a reference.
In the present work, a novel varying-order NURBS discretization method is proposed that provides a possibility to achieve controllable order elevation in the framework of isogeometric analysis. The method makes use of higher-order NURBS polynomials for the evaluation of the contact integrals. Lower-order of NURBS capable of representing the geometry exactly are used for the bulk computations. To achieve this, a higher-order NURBS layer, which accompanies a large number of degrees of freedom and matches with the bulk parametrization, is utilized as the contact boundary layer of the geometry. The isogeometric contact formulation with varying order NURBS discretization is presented in the nonlinear kinematic setting using the mortar method. Non-penetrability and tangential sticking constraints are regularized using the penalty method.
The consistency of the presented isogeometric mortar contact formulation with VO NURBS discretization is verified through the contact patch test. The performance and capabilities of the proposed discretization method are then demonstrated through two-dimensional frictionless and frictional contact problems, considering small and large deformations. Based on the obtained results, it can be concluded that the newly proposed varying-order NURBS discretization method displays a superior performance in terms of accuracy and efficiency compared to that of the standard NURBS discretization approach.
For the same mesh resolution, the proposed method requires a considerably lower computational cost to obtain identical results as that of standard NURBS discretization. The gain in the efficiency stems from the lower-order NURBS polynomials employed for the computation of the vast majority of the bulk domain that does not come into contact. This gain further improves as the mesh is refined.
It is next shown that the accuracy of the solution significantly improves on applying the additional steps of order elevation to NURBS contact layer. This is attributed to the presence of a large number of additional degrees of freedom across the contact interface which consequently improves the accuracy of contact computations even with a coarse mesh. It is also shown that the associated computational cost still remains considerably lower as compared to the standard NURBS discretization.
Refining the geometry using varying order NURBS is observed to be quite robust for the considered numerical examples. Additionally, a good convergence behaviour is obtained with the proposed discretization method. Simplicity of the current approach allows itself to be conveniently embedded into existing isogeometric contact codes.
Several extensions are considered in the near future. The extension of the proposed VO NURBS discretization method to three-dimensional contact problems within the context of isogeometric analysis is planned. An efficient quadrature technique [Duong2015] that adaptively refines the integration domain along the contact boundary of the geometries to further improve the integration accuracy of the contact forces and their tangent contributions with a very coarse mesh can also be incorporated in the current framework.
6 Acknowledgment
The authors gratefully acknowledge the support from SERB, DST under project SR/FTP/ETA-0008/2014. The authors would like to express their gratitude towards Prof. Roger A. Sauer, AICES RWTH Aachen University for his valuable comments.
\printbibliography


A 1v1 human only PVP Event (for levels 10-25). So get building new characters for the chance to win amazing rewards!
Realmud will be hosting a 2v2 PVP event on Saturday 26th July at approximately 6pm EST. You may enter the battles or watch them... or both!
A few happenings for the 4th of July weekend on Realmud!
It's that time again Realmud! Grab those cameras and start submitting entries into the 2014 Summer Screenshot Contest to win fabulous prizes!
Do you have what it takes to become a noble Lepucian? To battle great beasts and retrieve the stolen items? Realmud needs you!
Changes to guild chests and additions to guild houses!
Double XP has now been turned on, we hope you enjoy the weekend!
The crashes/warps previously affecting Realmud should now be fixed as of this morning. If you experience any please remember to report them to alastor@t4c.com stating the time of crash and if the website is also down.
The Cupids of Althea needs your help! Will you aid them in their quest to defeat the Cherubs of Hatred? This task is not for the weak of heart, if you think you have what it takes then help out... for you will be greatly rewarded if you prevail.


A government advisory body in the Czech Republic is working on a new law to legalize growing and consuming medical marijuana.
The experts have proposed that marijuana would be imported or grown locally by registered firms licensed for such activity, which is currently illegal.
The group also proposed Monday that all patients using marijuana would be registered.
The draft of the new marijuana bill will be completed in December. If approved by the government and parliament, the law could become effective by the middle of next year.
Some 8,000 Czechs have signed an Internet petition supporting the move, arguing that such marijuana use is legal in a number of European countries and the United States.


I was still in law school while pursuing my path into my sorority. That meant that I was still reading at least 100 pages of legal 'stuff' a week, studying for finals, preparing for a presentation, AND I was writing a 25 page paper (the memory alone makes me tired). I was still working my cases for the clinic, and assisting with our community service component. I was still at church for service. I was still in ministry school. I come out of that season, and walk right into bar prep…and a car with an attitude. My car was in the shop weekly of the time that I was preparing for the bar exam (with the exception of the final 2 weeks - I ran out of money & emotional energy), because a new component of my a/c system went out, one at a time.
If God told me, back in January that March - July would look like this, I probably would've walked into it with a defeated mindset, or bombarded Him with questions. Liiiiiike….preparing for the bar exam is stressful and time consuming enough. Why can't I have A/C in my little car?! Why can't I just study like everybody else? Wait…wait…You give me the chance to FINALLY be in this sorority…and You're telling me that this has to happen in one of the BUSIEST semesters of my entire law school career?! However, through that season, I learned that in order for God to expand your territory, He has to expand your view of your capabilities. Months ago, I wouldn't have believed that I was capable to do so much at one time. I have a very real hesitation of doing too much at my own detriment. Yet, today I look at challenges and say that if I could make it through that, I can make it through this. That…THAT is expansion.
I think that we often ask God to "enlarge our territory" without realizing what that expansion will require from us. We see the expansion as a solution to our current problems, but we don't consider what new problems it could cause ahead, especially if we're not prepared. Think about it: if you work 10 acres & suddenly have 100, you'll need more tools, more seeds, more time, etc. to be a good steward over that 100 acres than the 10. Sure, the harvest will be greater (that's where we stop & shout), but the work requirement will increase as well (I rarely see people authentically shout over this). The new level will require more from you than previous levels have. So while you're praying for upgrades & elevations, realize that your new tax bracket, your promotion, your marriage, your new home, your new level will require more from you than your current level does. That's not to scare you or stop you from reaching higher, but we have to stop expecting more out of God's hands, & not expecting more from our own. Why should God give you something new…to waste? Especially when His name is on it? Why should He give you more for you to treat the new the same way you treated the old? What will be different this time? How will you be different this time?
I believe that whenever God extends His hands to us, He expects us to be productive with what He's given us. God is productive in everything He does, & He expects productivity from us. Psalms opens with a declaration that everything a blessed person does will prosper. So my question is…what are you doing? It's important to know that prosperity is the fruit of purpose. Prosperity flows from purposeful action - actions that re-present God to those around you. Even if it's not your "call" inside of the walls of the church, your life is a re-presentation of God's power and ability to work on behalf of His people. God is strategic. He doesn't open doors or elevate without a mission, and that mission will expand His name throughout this earth. That mission, that dream, that prayer, will require work…from you. Yes, you'll reap a greater harvest, but it will likely require you to put in a greater investment.
Everything that I have - every degree, every dime, every word, every ounce of joy - I have because God invested it into me. I have many of the things I've asked for. I graduated. I'm in my sorority. I've taken the bar. I'm about to be a whole attorney! I'm in ministry school…and I have the responsibilities that come with each of those roles. With the expansion of territory comes the expansion of expectation. When your 'territory' expands, your faith has to expand. When your territory expands, your image of your capabilities has to expand. When your territory expands, your strength has to expand. There is, however, good news: you wont handle the increase by yourself. With every expansion, I've watched God breathe new life, new strength, and new vision into me - and He will do the same for you!
Awesome blog.....so very proud of your enlarged territory!!!


text:
/** \file
 * Base implementation of an ANTLR3 parser.
 *
 *
 */
#ifndef	_ANTLR3_PARSER_H
#define	_ANTLR3_PARSER_H

#include    <antlr3defs.h>
#include    <antlr3baserecognizer.h>

/** This is the main interface for an ANTLR3 parser.
 */
typedef	struct ANTLR3_PARSER_struct
{
    /** All superstructre implementors of this interface require a pointer to theirselves,
     *  whcih they can refernce using the super pointer here.
     */
    void			* super;

    /** A pointer to the base recognizer, where most of the parser functions actually
     *  live because they are shared between parser and tree parser and this is the
     *  easier way than copying the interface all over the place. Macros hide this
     *  for the generated code so it is easier on the eye (though not the debugger ;-).
     */
    pANTLR3_BASE_RECOGNIZER	rec;

    /** A provider of a tokenstream interface, for the parser to consume
     *  tokens from.
     */
    pANTLR3_TOKEN_STREAM	tstream;

    /** A pointer to a function that installs a token stream
     * for the parser.
     */
    void			(*setTokenStream)	(struct ANTLR3_PARSER_struct	* parser, pANTLR3_TOKEN_STREAM);

    /** A pointer to a function that returns the token stream for this
     *  parser.
     */
    pANTLR3_TOKEN_STREAM	(*getTokenStream)	(struct ANTLR3_PARSER_struct	* parser);

    /** Pointer to a function that knows how to free resources of an ANTLR3 parser.
     */
    void			(*free)			(struct ANTLR3_PARSER_struct	* parser);

}
    ANTLR3_PARSER;

#endif

redpajama_set_name: RedPajamaGithub


The attorney you choose to assist with your divorce, child custody dispute, or any other matter of family law can make a dramatic difference in the outcome of your case. A skilled lawyer can help simplify the proceedings and offer guidance at every stage of your case. At Elkouri Heath PLC, we understand the challenges that you may be facing, and we are equipped to provide the responsible representation you need while offering the personal attention you deserve.
Post-judgment modifications and order enforcement.
To learn more about our firm and how we can help you and your family, contact our office. Call 248-344-9700 for a free, no-obligation consultation today. Located in Novi, MI, our firm serves clients in Livonia, Livingston, Northville, Macomb, Canton, Washtenaw, Farmington Hills, Wayne County, Oakland County, and the surrounding areas.
Our attorneys can help you navigate the divorce process and will work with you in obtaining a favorable outcome.
An amicable solution to your divorce or family law matter may be possible through mediation or collaborative law.
We are dedicated to protecting your parental rights while promoting the best interests of your children.
Attorneys Susan Elkouri and Symantha Heath are accomplished family lawyers who have been serving clients in southeast Michigan for more than 20 years. During that time, we have developed a reputation as hardworking attorneys who know how to get results. With our experience, we recognize the importance of listening carefully to our clients so that we can customize a solution to meet their specific and unique needs.
Our attorneys are certified collaborative divorce lawyers and divorce mediators who understand the value of negotiation in family law proceedings. We facilitate amicable resolutions whenever possible, but we are also fully prepared to litigate your matter in court when necessary.
No matter what challenges arise, we will remain at your side throughout the process, ensuring your rights and best interests are fully protected.
During divorce you face some of the most difficult decisions of your life. After a consultation with Ms. Heath, I knew she was the attorney I would hire. Her professionalism carried through the whole process of getting divorced. From meetings, emails, phone calls, mediation and my final court date; I felt a confidence knowing I had Ms. Heath representing my best interests. I have and will continue to recommend Ms. Heath.
Words cannot express the professionalism Elkouri & Heath has given me in my time of need. I felt very confident and secured in court with Symantha Heath by my side. I couldn't imagine being represented by any other Firm. I am very pleased with the performance, support, professionalism and outcome of my divorce case. They exceeded all of my expectations. I'm very grateful and would recommend Elkouri & Heath to everyone.
I was recommended by a colleague who use Symantha in the past. I asked him if he knew a good divorce lawyer and the first and only person he mentioned was Symantha Heath in Novi. After speaking with her I knew immediately she was the one I needed fighting this divorce battle. She super exceeded my expectations. Any issues I ever have her office will be the one and only office I ever call.


More Than Sound produces and publishes media in the fields of mindfulness and conscious leadership-two areas they consider crucial to society's continued development.
More Than Sound's founder, Hanuman Goleman, was introduced to formal mindfulness meditation by Sayadaw U Pandita, Michele McDonald, and Steve Smith in 1989 at the first young adult retreat offered at the Insight Meditation Society (IMS) in Barre, MA. Now known as the Teen Retreat, it has been an introduction to mindfulness for hundreds of teenagers over the years. In 2007, Hanuman began volunteering as a discussion group facilitator at the Teen Retreat, and in the years since, he has been a part of introducing the transformative experience of mindfulness practice to young people. This work led Hanuman to take part in establishing a monthly young adult sitting group at Insight Pioneer Valley in Easthampton, MA.
Seeing the benefits that the changes brought about by mindfulness have in transforming basic quality of life in youth and adults alike has been a main drive behind the development of More Than Sound. They record and publish CDs, videos, and books from thought-leaders in the emerging field of affective neuroscience, from renowned mindfulness teachers, and experts in emotionally intelligent leadership. More Than Sound is dedicated to aiding in the continued integration of mindfulness practice in the secular world, as they believe that this union has potentially enormous benefit for both the prosperity and humanity of our shared future.
The opportunity to partner with The Center for Mindfulness at UCSD in offering the videos of their Bridging the Hearts and Minds of Youth conference was a natural next step for More Than Sound. This conference brings together a special community of professionals united around a common goal of helping our young people reach their potential and be happy, healthy, well-adjusted human beings who practice compassion, patience, equanimity and presence. Our recordings of the conference are a perfect way to broaden our community and educate others interested in introducing mindfulness techniques to our future generation.
To this same end, More Than Sound also offers practical mindfulness instruction from distinguished teachers. Their most recent release in this area is the CD, Working with Mindfulness, with mindfulness teacher and organizational management expert Mirabai Bush. Bush is the founder of the Center for Contemplative Mind in Society, which has led mindfulness trainings for thousands of employees and executives of major corporations and non-profits, including Google, Monsanto, Hearst Publications, and the Fetzer Institute.
Bush was also a key contributor to Google's now-famed Search Inside Yourself curriculum. Working with Mindfulness is a series of practices based on traditional mindfulness practice but crafted around a work environment. There is mindful e-mailing, for example, coping with change, and managing negative emotions. Participants in Bush's programs through the years have consistently reported reduced stress, increased productivity, more creative problem solving, and improved relationships – all essential for a top-performing workplace, and for happier lives.
More Than Sound is proud to have a working partnership with the UCSD Center for Mindfulness and to be involved with the important work of Bridging the Hearts and Minds of Youth. Sharing the work of these educators, researchers and therapists is way to be of further benefit to the continued understanding and practice of mindfulness techniques in our lives.


text:
Tag: brain
The Lone Gunmen (2001) – Three Men and a Smoking Diaper, and Madam, I'm Adam
Chris Carter has Frohike (Tom Braidwood), Langly (Dean Haglund) and Byers (Bruce Harwood) tackle politicians in Three Men and a Smoking Diaper, which first aired on 23 March, 2001. The boys are investigating a senator, Jefferson (Christopher Rich), who may have had a relationship with one of the people on his campaign and later died…
The X-Files (1999) – Hungry, and Millennium
Vince Gilligan delivers the first monster-of-the-week episode of the seventh season with Hungry, an episode that first aired on 21 November, 1999. Mulder (David Duchovny) and Scully (Gillian Anderson) are investigating a strange murder in California, a body is recovered with no brain matter, and a strange hole that Mulder thinks may have been a…
The X-Files (1999) – The Sixth Extinction, and The Sixth Extinction II: Amor Fati
Series creator Chris Carter pens the seventh season opener of The X-Files, which premiered on 7 November, 1999. Scully (Gillian Anderson) is still in West Africa, on the Ivory Coast, investigating the strange, possible extraterrestrial structure (craft?) that the ocean has revealed. The entire thing is covered in text that seems to touch on all…
Phantasm III: Lord of the Dead (1994) – Don Coscarelli
The Tall Man (Angus Scrimm) returns to the screen for a third time in the second sequel to the 1977 cult phenomenon, Phantasm. The film not only gives viewers a quick recap, it runs us right up to the cliffhanger conclusion of the second film, and then welcomes A. Micheal Baldwin back to the role…
Chuck (2007) – Pilot, and Verus the Helicopter
This week I begin a revisit with the awesomeness that is the television series, Chuck. I remember being completely enraptured with it from the first episode, which debuted on 24 September, 2007 – right when I needed some fun and joy. The pilot for the series was written by series creators Josh Schwartz and Chris…
Space: 1999 (1976) – Ring Around the Moon, and Missing Link
Ring Around the Moon is the first episode up this week, as I continue my travels with Moonbase Alpha. Written by Edward di Lorenzo this story first debuted on 15 January, 1976. A strange yellow energy field has an adverse effect on one of the Alphan techs, as a strange planet pulls it into temporary…
Star Trek: Deep Space Nine (1994) – The Maquis: Part II, and The Wire
Station log: stardate unknown Last week's cliffhanger revelation about Cal Hudon (Bernie Casey) impacts Sisko (Avery Brooks) this week as The Maquis: Part II comes to a conclusion. Written by Ira Steven Behr from a story by Rick Berman, Micheal Piller, Jeri Taylor and Behr, the episode continues to lay foundation work for the next…
Star Trek: The Next Generation (1991) – The Nth Degree, and Qpid
Captain's log: stardate 44704.2 Airing on 1 April, 1991, The Nth Degree, written by Joe Menosky, brought back fan favourite Reginald Barclay (Dwight Schultz). Barclay is slowly finding his way out of his shell, working with Crusher (Gates McFadden) on some theatre workshops. He's slowly finding his way. The Enterprise arrives at the Argus Array…
Ghost in the Shell (2017) – Rupert Sanders
Paramount Pictures' live action adaptation of the classic anime, Ghost in the Shell, hits blu-ray and DVD today. I am going to eschew any discussion of the white-washing controversy surrounding the film's production, and just focus on the movie itself. I love the original anime, and constantly saw it as kin to the cinematic version…
Star Trek: The Original Series (1967) – The Squire of Gothos and Arena
Captain's log: stardate 2124.5 The Squire of Gothos. Oh man, what a fun episode. Penned by Paul Schneider this episode had it's first airing on 12 January, 1967. Captain James T. Kirk (William Shatner) and Lt. Hikaru Sulu (George Takei) vanish from the bridge, and when Spock (Leonard Nimoy) sends a landing party, led by…

redpajama_set_name: RedPajamaCommonCrawl


When it comes time to buying nursery room must haves for a new baby, no matter who you ask or what you read, you'll likely see the same list of items: crib, diaper pail, rocking chair. When it came time for me to assess these lists for my own growing family's needs, I had to put my foot down. I couldn't argue the crib and I couldn't figure out a workaround for a diaper pail , but the chair, the bulky, slipcovered monstrosity of swaying furniture? Absolutely not. I would not be sitting in one of those. My logic was clear: I don't sit in one now; why on earth would I want to sit on one once I had a baby?


Since 2000 Donation Line has been one of the largest and most trusted Vehicle Donation Centers in the United States.
Accredited BBB member since 2000, BBB A+ Rating, the highest in the car donation industry.
Donation Line steers clear of questionable gimmicks which would jeopardize a donors tax deduction and a charity's tax deductible status. Come-ons which we avoid include; free vacations, cash payments and schemes claiming the donor can take a blue book tax deduction when 98% of the time they will not be entitled to such a deduction. Remember, if it sounds too good to be true it probably is and thus should be avoided.
Donate My Car Now – complete and submit our simple and secure vehicle donation form or call us toll free at 1-877-227-7487, 24 hours, 7 days per week. Phones are answered by our experienced and trained operators.
You will be contacted by our towing agent within 2 business days. Rush pick-up can often be accommodated.
Pick-up in all 50 states.
Your auto donation will be removed by a professional towing company quickly and hassle free.
Your tax return ready letter will sent by the charity within 6-8 weeks of pickup.
Making a car donation is faster, easier and safer than selling your vehicle.


Those searching for the right Lincoln porta potty rentals just ran into some luck because working together with portable toilets recently got easier. A few years ago searching for a great deal was more or less a nightmare, but in these days you are able to only phone www.NaWaterSystems.com and have your perfect solution setup in minutes. Fast deliveries, very low costs and customer care that makes our rivals look like rookies.
The majority of our rivals merely boast about how great they are and then they fail their customers without ever offering evidence to their presumed abilities. We, on the other hand, will reveal just why we're considered the most truly effective porta potty rental providers in Lincoln! Read this page and obtaining a temporary restroom in this part of Nebraska's going to be easier!
There should be no question concerning whether finding a temporary toilet is worth it, aside from why you're visiting our web page. Whether you're a building company, an event organizer, or simply wanting to keep your property clean for the next family gathering / bbq, you're in the proper position and you'll be very glad you encountered us.
Naturally, the top customer of any Lincoln porta potty rental business is represented by construction guys. There in fact is no way one could run a fruitful and powerful construction site without renting porta toilets in Lincoln certainly not without missing deadlines and ruining their reputation. Each and everyone of our customers who are renting portable restrooms from us are very happy with their conclusions and it's all for a very good reason: workers are much happier and more productive when they discover their needs are looked after. Imagine working 12 hours shifts in a filthy, cold area without having a bathroom nearby doesn't seem like you'd be happy, does it?
Low priced Lincoln porta pottie Accessible Today!
Whether we are happy about it or not, every once in a little while it's our turn to host the family reunion and you know what that means: having a great deal of people the majority of whom you don't actually like – come to your house. By finding a porta-potty rentals in Lincoln you could prevent the undesired situation where each one of these people end up using the same toilet you and your loved ones use every single day.
Nevertheless the best part about this idea is the fact that everyone else will like you because of it! To begin with, it's an originality and most people have not used this type of bathroom before you'll be the forward thinking person in the household! Furthermore, they'll know you did it for their own comfort and aunt Susie will certainly appreciate a porta jon the undeniable fact that she doesn't have to go all the way upstairs to utilize the bathroom!
You don't need us to inform you this is not the type of support you must spend a great deal of energy and money on. We offer the fastest and most dependable Lincoln porta-potty rental services you'll ever find in Nebraska and we're eagerly waiting to work with you. Think you're not big or essential enough to deserve this type of premium support? Wrong! We work with clients of all sizes from all around Lincoln's surroundings and each and everyone one of them gets exactly the same undivided focus that made us market leaders.
Renting from us is, in all seriousness, as easy as it gets. All you have to do is grab your phone, call (888) 353-2641 inform us when and where you need temporary sanitation and our team is going to do the rest! Don't know just what you will need? No problem! Our experts are standing by to answer all of your questions and suporta pottyly the necessary assistance. Getting high quality, clean and efficient porta potty rental in Lincoln has become easier than ever!


With verses full of metaphors and intriguing wordplay as well as with its catchy hook, "Isale Eko" is a tune which defines the Young Bullet Boiz as a group. The song was produced by Elis, mixed and mastered by Dr Jazz. Enjoy!
I never loved hip-hop. Never will I try that rap, saying lots of words in split seconds that can give you an award as best in speech.


text:
How to Prepare for the Cookieless Era
Digital Marketing Technology
2021-05-10 2021-06-16 Hana Nozaki
Eversince Google announced that third-party cookies will be disabled in the Google Chrome browser by 2022, increased attention has been drawn towards Cookieless matter in the digital advertising industry.
However, a new study by Aroscop and Brand Equity that polled over 450 marketers, advertisers, publishers, and technology providers, found that only 22% of the respondents believe that a cookieless future may have a severe impact on brand building and only 8% of the respondents have deployed alternate solutions to prepare for the shift.
Disabling cookies is a topic that should be accurately understood and appropriate action to be taken by everyone involved in digital marketing. Read this article and find out what Cookieless is all about and how you can prepare for the new era.
1 What is Cookie?
2 What are the first-party and third-party cookies?
3 Recent movements regarding third-party cookies
4 Impact of disabling third-party cookie on the industry
4.1 1. Audience Targeting
4.2 2. Retargeting Advertising
4.3 3. Conversion Measurement
4.4 4. Frequency Control
5 Impact on each stakeholder
5.1 Users
5.2 Advertisers
5.3 Publishers
6 Practical Solutions
6.1 First party data
6.2 Second party data
6.3 New user identify framework
6.4 Google Chrome's Privacy Sandbox
6.5 Advertising on Premium Media
6.6 Contextual targeting
What is Cookie?
Cookie is a text file with a small piece of data. When we visit a website, the server sends cookies to the browser to record the data such as the number of times to visit the site and how we behave on pages. The cookies will be stored in the user's browser for a certain period of time and the data will be utilized for the next site visit. For example, cookies help browsers to save login information, and products added to the cart on online shopping stores.
What are the first-party and third-party cookies?
There are two types of cookies: first-party and third-party cookies. From a technical perspective, there is no real difference between the two types of cookies. The difference is defined by who issues the cookie and for what purpose it is used.
Cookies that are issued by the website which the users are visiting are called first-party cookies. These cookies are used by the website owners to collect analytical data, remember user preferences and provide a personalised experience on their web site.
On the other hand, third-party cookies are issued by entities other than the website that the users are visiting. It's often the providers of advertising on the web site as the image ow shows. Third-party cookies are used for cross-site ad tracking, wider audience profiling/targeting and personalisation in advertising.
Recent movements regarding third-party cookies
Thanks to third-party cookies, users can see personalised advertising according to their preferences. However, there are people who don't want their data to be collected without noticing and used for targeting advertising based on cookies issued by the entities other than the web sites they visit.
In view of this, several countries have already enacted laws regulating the use of third-party cookies to protect consumer privacy. The EU General Data Protection Regulation(GDPR) and California Consumer Privacy Act (CCPA) are the most famous examples. While in Asia, the Personal Data Protection Act (PDPA) in Singapore, the Personal Information Protection Act (PIPA) in Korea, the PDPA in Thailand and China's Cybersecurity Law (CSL) have also been enacted.
In the meantime, browser providers are starting to move towards disabling third-party cookies. Apple, the provider of Safari, launched ITP (Intelligent Tracking Prevention) as a feature of Safari in September 2017, putting strict restrictions on the use of third-party cookies. Mozilla, the provider of the Firefox browser has turned on blocking of third-party trackers by default in Firefox for desktop and Android since September 2019.
However, the largest impact comes in the future when Google Chrome (which has more than 70% of browser share in Asia) sunsets the use of third-party cookies in 2022.
Source: gs.statcounter.com
[Column] Is this different from the issues surrounding iOS14?
Another hot topic related to user privacy and data usage is Apple's announcement that app developers need to receive the user's permission through the AppTrackingTransparency framework to track them or access their device's advertising identifier (IDFA) from iOS 14.5.
IDFA is the unique ID to identify iOS devices and it's mainly used for measurement and optimisation of app advertising campaigns. So far, users have been able to reset their IDFA and opt out of ad measurement and ad personalisation using their ID. However, starting with iOS 14.5, each app needs to ask users for permission to collect and use their data (change to opt in scheme). This will significantly reduce the amount of data and will have a huge impact on app advertising campaigns.
The sense of the issue behind this is the same as the discussion around third-party cookies. It's for putting the control of data use back in the hands of the users. Briefly, the difference is that third-party cookies are the technology for the browser, whereas IDFA is for apps.
Impact of disabling third-party cookie on the industry
The disabling of third-party cookie will affect the digital advertising industry in 4 main aspects: audience targeting, retargeting, conversion measurement and frequency control.
1. Audience Targeting
The audience targeting features offered by advertising platforms rely on the data of online user behaviour stored by third-party cookies. As major browsers will block third-party cookies, the amount of user data that advertising platforms will be able to capture and utilise for targeting will be reduced.
2. Retargeting Advertising
Retargeting advertising is generally recognised as an advertising method that is more likely to lead to conversions, because it allows advertisers to reach people who are already interested in their products or services. By embedding retargeting tags issued by the advertising platform into the website, advertisers can store the visitors data and deliver the advertising outside of the site. However, retargeting ads also use third-party cookies, which means that it will no longer be available in near future.
3. Conversion Measurement
Even if third-party cookies are disabled, it is still possible to measure conversions if users enter your website via advertising and make purchases without leaving the site. However, in many cases, users will search for products and visit the product pages multiple times before making purchase decisions. If third-party cookies are disabled, you will no longer be able to measure attribution from ads other than the last click before conversion, and we will probably see fewer conversions from ad campaigns.
4. Frequency Control
Advertisers tend to show the same ad creative to a user for a limited number of times per day/week. And, this frequency control feature relies on third-party cookies. Without third-party cookies, as there is no way to do frequency control yet, ad experience is going to be worse.
Impact on each stakeholder
Here we look at the impact of disabling third-party cookies will have on each stakeholder in the digital advertising industry.
Internet users will have more control over their online privacy. On the other hand, they will be more likely to encounter advertising that they are not interested in, due to the difficulty of advertising personalisation.
As mentioned earlier, advertisers will no longer be able to use audience targeting and retargeting method using third-party cookie technology, so they will have to explore new ways to reach their target audience.
It is also predicted that more advertisers will reallocate their performance advertising budgets to awareness and branding marketing activities.
The audience data gained from third-party cookies has helped to increase the value of the ad inventory. Disabling third-party cookies would lower CPM and reduce revenue for publishers. A study by Google, which disabled browser cookies for some users and looked at the impact it had on publishers' revenues, found that publishers' revenues fell by 52% on average.
While a perfect alternative to cookies has yet to be established and is still being explored, here are some ways in which advertisers and publishers should expect to make use of them.
First party data
Publishers and brands are starting to obtain user data without depending on cookies, for example, they ask users to sign up to access their premium contents.The sign up form can include email address, contact number, as well as occupation, income range, interests and so on. Marketers can utilize these data for their own marketing.
Second party data
Project Rearc* encourages marketers to explore the use of second party data, which is sharing the first party data between different, trusted, non-competing organisations.
Second-party data refers to first-party data from one business that was given exclusively to another business. This exchange of data may occur between businesses, marketers, platforms or publishers. The use of second-party data represents an opportunity for marketers to leverage each other's data and come up with mutually beneficial arrangements. Ultimately, customers should be the main beneficiaries of such partnerships because their favourite brands can offer more relevant and personalized experiences.
Source: iabseaindia.com
*Project Rearc is an initiative introduced by IAB and IAB Tech Lab. Stakeholders across the digital advertising and media supply chain are working together to propose data uses which do not rely on third-party cookies, and try to find new privacy-friendly solutions.
New user identify framework
To keep the healthy ecosystem in the digital advertising industry, the development of new frameworks for user identification is being explored. In most cases, publishers, advertisers and ad tech companies work together to develop new ID frameworks to continuously offer optimized advertising experience.
▼Leading framework for user identify
To create cookieless targeting capability, these ID frameworks are going to identify each user that they are currently engaging with or delivering ads across multiple touch points. Each of these users will be given an anonymous identifier by using hashed first party data by publishers and advertisers such as email address, contact number, and online/offline behavior.
This solution should support transparency and privacy control so that users have choice over the use of their data and they can choose to opt in or out, also allowing them to customize user experiences.
FreakOut has also joined the Unified ID 2.0 initiative led by theTradeDesk to work towards a better approach to consumer identity across the open internet.
[LINK] Unified ID Solution 2.0 | The Trade Desk
Google Chrome's Privacy Sandbox
Privacy Sandbox is a new advertising system for Google Chrome browser proposed by Google in 2019 that will replace third-party cookie while protecting user privacy.The detailed mechanism is still under discussion, but at present, the following APIs are being considered for use.
Advertising on Premium Media
Before the third-party cookie enabled programmatic media buying, media category and contents targeting were commonplace. Advertising on premium media that require users to log in to read quality editorial contents, or vertical media that have apparent user interests, enables to approach categorised groups of users without relying on audience targeting.
Contextual targeting is a solution that is attracting particular interest as an alternative to third-party cookie based audience targeting.The intention for contextual targeting is to drive user engagement by serving ads that are relevant to the content being consumed.
With the recent improvement of machine learning, contextual targeting capabilities have become much more intelligent, resulting in a move beyond simple keyword, category, and inclusion list targeting. Meanwhile, creative optimisation is now available which allows you to choose the most relevant ad from a range of materials depending on the content of the surface.
In addition, contextual targeting solutions for not only text based articles, but also video contents are now offered that can understand the context of videos and play relevant video ads.
Privacy regulation is an irreversible trend, but it is essential for making the internet a better place for consumers. All stakeholders in the industry should take this issue seriously in order to build a continuous relationship of trust with consumers.
Keep up with the ever-evolving solutions for the cookie-less era and take the necessary measures for each organization, while keeping privacy at the top priority.
Only 8% of Advertisers Prepared for a Cookie Less Future: Data Reveals
What's the Difference Between First-Party and Third-Party Cookies?
Safari ITP: Intelligent Tracking Prevention Version 1.0 to 2.3
How the cookie crumbled: Marketing in a cookie-less world
THE DEATH OF THE 3RD PARTY COOKIE AND TRACKING AS WE KNOW IT
Building a privacy-first future for web advertising
WTF is Google's Privacy Sandbox?
Digging into the Privacy Sandbox
What's Old is New Again: The Return of Contextual Targeting
Statcounter – Browser Market Share Worldwide
[OUR LEADERS] Yu-Wen Huang, Vice President, FreakOut China
[OUR LEADERS] Hiroshi Okada, Director of Cross Border Marketing Division
Social Commerce in the Southeast Asia (2020)
Generation Z Characteristic and How To Catch Their Attention