text:
12 Oils Of Ancient Scripture For Emotional Healing
I recently attended a workshop on the 12 Oils of Scripture, hosted by Cherie Ross. It was amazing! Her knowledge and experience are priceless, and her love for the oils and nature is very passionate. I'll leave this very brief for now, because I'm still processing.
Ever since this class, in which we studied and used all 12 oils, I have been undergoing a very rapid emotional clearing of very old wounds in my mental, emotional, and spiritual bodies that have kept me stuck and afraid of love for many years.
I have been doing extensive clearing every day, relationships are getting down to the core issues, old wounds are coming to the surface very quickly to be dealt with once and for all.
The power these oils have to affect the brain, memory, DNA, cellular structure, and the physical body is astounding. They also help us to connect to our divine source.
We have only just begun to understand the significance of these oils.
Additional keyword(s) assigned by the editor: anxiety, anxious, believe, calm, calming, childhood, divorce, divorced, emotion, emotions, fear, fears, marriage, moods, panic, sorrow, sorrows, stress, stressed, stressful.
1. Associated topics: mental,mood-swings,emotions-/-feelings — "The present study indicated that lavender aromatherapy as a potential therapeutic modality could alleviate premenstrual emotional symptoms, which, at least in part, is attributable to the improvement of parasympathetic nervous system activity. This study further implies that HRV could evaluate the efficacy of aromatherapy using various fragrances to relieve premenstrual symptoms, and ultimately, support the mind and body health of women." Link
2. Associated topics: stress-/-tension-/-burnout,anxiety-/-worry,depression-/-sadness-/-hopelessness-/-sorrow — "After inhalation of clary sage oil, cortisol levels were significantly decreased.... Thyroid stimulating hormone was also reduced.... Clary sage oil has antidepressant-like effect...." Link
3. Associated topics: stress-/-tension-/-burnout,anxiety-/-worry,depression-/-sadness-/-hopelessness-/-sorrow — "Lavender, mint [peppermint], orange, rose, chamomile, rosemary, and sage were used.... Depression levels in the touch-music-aroma therapy group... showed a larger decrease than in the... control groups [that did not include aromatherapy].... [FMS] symptoms such as restless sleep, headache, morning fatigue, exhaustion, feeling like crying, and bowel complaints were also significantly reduced." Link
4. Associated topics: mental,mood-swings,emotions-/-feelings,anxiety-/-worry,depression-/-sadness-/-hopelessness-/-sorrow — "Beta-Caryophyllene [component of cannabis, clove, copaiba], a CB2 [cannabinoid] receptor agonist produces multiple behavioral changes relevant to anxiety and depression in mice.... these preclinical results suggest that CB2 receptors may provide alternative therapeutic targets for the treatment of anxiety and depression. The possibility that BCP may ameliorate the symptoms of these mood disorders offers exciting prospects for future studies." Link
5. Associated topics: mental,mood-swings,stress-/-tension-/-burnout,anxiety-/-worry,depression-/-sadness-/-hopelessness-/-sorrow — "A number of essential oils are currently in use as aromatherapy agents to relieve anxiety, stress, and depression. Popular anxiolytic oils include lavender (Lavandula angustifolia), rose (Rosa damascena), orange (Citrus sinensis), bergamot (Citrus aurantium), lemon (Citrus limon), sandalwood (Santalum album), clary sage (Salvia sclarea), Roman chamomile (Anthemis nobilis), and rose-scented geranium (Pelargonium spp.)." Link
6. Associated topics: mental,mood-swings,stress-/-tension-/-burnout,anger-/-frustration,anxiety-/-worry,depression-/-sadness-/-hopelessness-/-sorrow — "Most studies, as well as clinically applied experience, have indicated that various essential oils, such as lavender, lemon and bergamot can help to relieve stress, anxiety, depression and other mood disorders. Most notably, inhalation of essential oils can communicate signals to the olfactory system and stimulate the brain to exert neurotransmitters (e.g. serotonin and dopamine), thereby further regulating mood." Link
7. Associated topics: stress-/-tension-/-burnout,anxiety-/-worry,depression-/-sadness-/-hopelessness-/-sorrow — "The ylang ylang oil caused a significant decrease of blood pressure and a significant increase of skin temperature. At the behavioral level, subjects in the ylang ylang oil group rated themselves more calm and more relaxed than subjects in the control group. These findings are likely to represent a relaxing effect of the ylang ylang oil and provide some evidence for the usage of the ylang ylang oil in aromatherapy such as causing a relief of depression and stress in humans." Link
8. Associated topics: mental,mood-swings,emotions-/-feelings,stress-/-tension-/-burnout,anxiety-/-worry — "Lavender essential oil has been used as an anxiolytic [anxiety] drug, a mood stabilizer, a sedative, spasmolytic [muscle spasms], antihypertensive [high blood pressure], antimicrobial, analgesic [pain] agent as well as a wound healing accelerator.... The present study suggests that inhalation of lavender essential oil may be an effective and safe treatment modality in acute management of migraine headaches." Link


We've set up a work schedule that explains the right time to do everything, based on your (and your co-workers') circadian clock, research on productivity cycles, and other timing insights. Before long, pushing through afternoon grogginess while on deadline will be a thing of the past.
If you're hoping for a reply to your email (and who isn't?), send it during nonworking hours. Emails sent between 6 AM and 7 AM., or around 8 PM., are about 45% more likely to elicit a response, according to research from Yesware, a company that creates tools for sales teams.
Conflicted about whether it's time to let the new hire go? Worried about reporting a colleague's bad decision to higher-ups? Make ethical judgments like these in the morning. That's when the "morning morality effect" is in action, according to research from Harvard University and the University of Utah.
Researchers found cheating among undergraduates was more prevalent in the afternoon, leading them to conclude people are more likely to engage in unethical acts later in the day. This might be because our capacity for self-control, like physical energy, can deplete throughout the day as you make everyday decisions.
Now's the time to put together that new business proposal, report financial earnings, or handle another responsibility that requires your full attention. "When you first get to the office in the morning is when you're going to be freshest, and that's the ideal time to do those tasks that are most attention-demanding," Spencer says. Resist the urge to waste your alertness on mindless tasks like sorting through your AM emails. If it's too hard to ignore, tools like Inbox Pause keep new emails from coming in—temporarily, of course.
Your coworkers' brains are also more alert, so this is a good time to schedule a team brainstorm. Research from Robert Matchock, an associate professor of psychology at Pennsylvania State University, found most of us tend to be easily distracted between noon and 4 PM.
Need to get that easy-breezy memo out the door? Right after lunch is the time to do it. That's when our energy levels sink, typically between 1 PM and 3 PM "We sometimes have a need for a midday nap, or we feel groggy after lunch," Spencer says. "It's not necessarily because of a heavy meal—we have a natural dip in our alertness in the afternoon." Instead of struggling to focus on a key project when you're in an energy slump, Spencer suggests filling that time with simple projects that require less of your attention, like catching up on email and voice mail.
Your judgment isn't at its sharpest this late in the workday because you've likely been depleting your energy on more attention-demanding tasks until now. (And let's face it, you might be more focused on going home soon, Di Vincenzo points out). That's why it's best to avoid the late PM hours for interviews, no matter if you're the interviewer or interviewee. Take it from the research: When five similarly qualified candidates interviewed on the same day, the last ones to be interviewed received the worst feedback, finds a paper from Wharton School and Harvard Business School.
Release work stress and rebound from sitting all day by scheduling your workout at this time, when your body temperature reaches its peak. Studies suggest certain muscles are strongest now, especially between 4 PM and 6 PM This might be why more world-record-breaking athletic performances occur in early evening, researchers believe.
Ready to see what the hype about adult coloring books is about, or want to start writing the next great American novel? Consider 7 PM the golden hour for creativity. A 2011 study published in Thinking & Reasoning found we do our best open-ended, creative thinking when we're tired. As a bonus, these after-work projects can make you a better employee. A report from Quantum Workplace and Limeade found employees with a healthy work-life balance are 20% more engaged in their job.
Additionally, avoid using all screen devices (cell phones, TVs, and computers), or at the very least set the artificial light to low. "If you really want to shift your clock, you have to restrict access to light," Spencer says. If you must watch a Netflix show on your computer as you're winding down, try downloading f.lux, a software that reduces your computer screen's output of sleep-disrupting blue light as you get closer to bedtime.


text:
\section*{NOMENCLATURE}
\begin{tabbing}
	\bfseries left \quad \=\bfseries center \quad \=\bfseries right \quad \=\bfseries paragraph \kil
	$\mathbf{B}$ \> \quad Left Cauchy-Green tensor \\
	$\mathbf{B}_{i,j}$ \> \quad Subordinate eigenprojections of $\mathbf{B}$  \\
	$\mathbf{D}$ \>\quad Rate of deformation tensor \\
	$\mathbf{D}^e$ \>\quad Rate of deformation tensor of elastic part  \\
	$\mathbf{D}^{tr}$ \>\quad Rate of deformation tensor of transformation part \\
	$\mathbf{F}$ \>\quad Deformation gradient \\
	$\mathbf{L}$ \>\quad Velocity gradient\\
	$\mathcal{S}$ \>\quad Effective compliance tensor\\
	$\mathcal{S}^A$ \>\quad Compliance tensor for austenite phase\\
	$\mathcal{S}^M$ \>\quad Compliance tensor for martensite phase\\
	$\Delta \mathcal{S}$ \>\quad Compliance tensor phase difference\\
	$\mathbf{W}$ \>\quad Anti-symmetric part of velocity gradient\\
	$\mathbf{X}$ \>\quad Position vector in reference configuration\\
	$\bm\Lambda$ \>\quad Transformation direction tensor\\
	$\bm\Lambda^{fwd}$ \>\quad Forward transformation direction tensor\\
	$\bm\Lambda^{rev}$ \>\quad Reverse transformation direction tensor\\
	$\bm{\Omega}^{log}$ \>\quad Logarithmic spin\\
	$\mathbf{h}$ \>\quad Logarithmic strain of Eulerian type \\
	$\mathbf{h}^{tr}$ \>\quad Transformation strain \\
	$\mathbf{h}^{tr-r}$ \>\quad Transformation strain at reverse point \\
	$\bar{\mathbf{h}}^{tr-r}$ \>\quad Effective transformation strain at reverse point \\
	$\mathbf{x}$ \>\quad Position vector at current configuration\\

	$\bm{\Upsilon}$ \>\quad Internal state variable set\\
	$\bm{\uptau}$ \>\quad Kirchhoff stress tensor \\
	$\bm{\uptau}'$ \>\quad Deviatoric part of Kirchhoff stress \\
	${\bar\uptau}^{'}$ \>\quad Effective Kirchhoff stress \\
	$\bm\alpha^A$ \>\quad Second order thermal expansion for austenite   \\
	$\bm\alpha^M$ \>\quad Second order thermal expansion for martensite  \\
	$\Delta\alpha$ \>\quad Thermal expansion phase difference\\
	$\mathcal{D} $ \>\quad Dissipation energy\\

	$A_s$ \>\quad Austenite phase transformation start temperature\\
	$A_f$ \>\quad Austenite phase transformation finish temperature\\
	$M_s$ \>\quad Martensite phase transformation start temperature\\
	$M_f$ \>\quad Martensite phase transformation finish temperature\\
	$G$ \>\quad Gibbs free energy\\
	$H^{max}$ \>\quad Maximum transformation strain\\
	$T$ \>\quad Temperature \\
	$T_0$ \>\quad Temperature at reference point \\
	$Y$ \>\quad Critical thermodynamic driving force \\

	$a_1,a_2,a_3$ \>\quad Material parameters in hardening function \\
	$c$ \>\quad Specific heat \\
	$f(\xi)$ \>\quad Hardening function \\
	$s$ \>\quad Specific entropy \\
	$s_0$ \>\quad Specific entropy at reference state \\
	$\Delta s_0$ \>\quad Specific entropy phase difference \\
	$u$ \>\quad Internal energy\\
	$u_0$ \>\quad Internal energy at reference state\\
	$\Delta u_0$ \>\quad Internal energy phase difference \\

	$\Phi$ \>\quad Transformation function\\
	$\rho$ \>\quad Density at current configuration  \\
	$\rho_{0}$ \>\quad Density at reference configuration  \\
	$\xi$ \>\quad Martensite volume fraction  \\
	$\nabla$ \>\quad Gradient operator\\
	$\chi$ \>\quad Deformation mapping function\\
	$\lambda_i,\lambda_j$ \>\quad Eigenvalues of $\mathbf{B}$  \\
	$\pi$ \>\quad Thermodynamic driving force\\
\end{tabbing}

\section*{INTRODUCTION} \label{sec:intro}

Shape Memory Alloys (SMAs), known as an intermetallic alloys with the ability to recover its predefined shape under specific thermomechanical loading, has been widely aware of working as actuators for active/smart morphing structures in engineering industry. Because of the high actuation energy density of SMAs, structures integrated with SMA-based actuators has high advantage in terms of trade-offs between overall structure weight, integrity and functionality. There has been existing fatigue, damage\cite{wheeler2014characterization,Darren2018} and preliminary corrosion research\cite{MM2018} into SMAs over the past several decades in order to realize SMA-based actuators into extensive industry applications.

A substantial of SMAs constitutive theories at continuum levels have been proposed, the majority of them are within small deformation regime based on infinitesimal strain assumption. Some thorough review of shape memory models can be found from Boyd and Lagoudas\cite{boyd1996}, Birman and November\cite{birman1997}, Raniecki and Lexcellent \cite{raniecki1992,raniecki1998}, Patoor et al.\cite{patoor2006,patoor1996}, Hackl and Heinen\cite{hackl2008}, Levitas and Preston \cite{levitas1998} etc.. The aforementioned models are able to predict SMAs response accurately within infinitesimal strain regime. However, recent publication has reported that shape memory alloys can reversibly deform to a relatively large strain up to 8\% \cite{jani2014,shaw2000}, and also repeated cycling loading has been reported to induce irrecoverable transformation induced plasticity strains up to 20\% or more\cite{wheeler2014,Xu2017trip}. Strain regime in cracked SMA specimen can also go up to 8\%\cite{BH1,BH2,BH3,BH4}. In addition to such relatively large strains, SMAs-based devices may also undergo large rotations during its deployment. Combining above two factors, it is indispensable to develop a constitutive model based on finite deformation framework to provide accurate predictions for these SMA-based actuators under large deformations.

Much efforts has been devoted to proposing such a constitutive model for SMAs at finite deformation framework. Following finite deformation theory, two commonly accepted kinematic assumptions are usually adopted for the model development. One is the multiplicative decomposition on deformation gradient, and the other one is the additive decomposition on the total rate of deformation tensor. The first one is simply based on classic crystal-plasticity theory. In contrast, the second one is following energy conservation principle that the total energy provided from the outside can be additively divided into a recoverable part plus a dissipative part.

Existing approaches based on the multiplicative decomposition to formulate a finite strain constitutive model for SMAs can be found from literature Auricchio \cite{auricchio1997,auricchio2001}, Arghavani et al.\cite{arghavani2011,arghavani2011improved,arghavani20103d}, Thamburaja and Anand\cite{tham2010,tham2001}, Reese and Christ\cite{christ2009,reese2008} etc.. However, the complexity of this model type and its high computational cost hinders its wide usage for industry application analysis that involved with a large amount of trial and error computation. In contrast, finite strain constitutive models based on additive composition achieves a much simpler model structure and easier implementation procedures, which enables it gaining a lot popularity and is commonly used in current available commercial finite element analysis softwares, such as Abaqus and ANSYS. However, this model types requires to adopt an objective rate in its rate form hypoelastic constitutive equation to achieve the principle of objectivity. A number of objective rates, such as Zaremba-Jaumann-Noll rate, Green-Naghdi-Dienes rate and Truesdell rate etc., have been proposed to meet this objectivity goal. However, those objective rates aforementioned are not real 'objective' for their failure to integrate the rate form hypo-elastic equation to deliver a free energy based hyperelastic stress-strain relation\cite{xiao2006}. Therefore many spurious phenomenons, such as artificial residual stress accumulation and shear stress oscillation, are often observed even for indissipative elastic material undergoing closed path cyclic loadings.

It was not until the logarithmic rate proposed and the proof conducted by Xiao et al.\cite{xiao1997,xiao1997hypo}, Bruhns et al.\cite{bruhns1999self,bruhns2001large,bruhns2001self} and Meyers et al.\cite{meyers2003elastic,meyers2006choice}, that such self-inconsistency issue related to objective rates has been resolved. In their mathematical proof from publication\cite{xiao1997} in the year of 1997, it was shown that: the logarithmic rate of logarithmic strain of its Eulerian type is exactly identical with the rate of deformation tensor, and logarithmic strain is the only one among all other strain measures enjoying this important property. This new development in finite deformation theory not only provides consistent solutions to classical plasticity problems for metallic material, but also sheds lights on the development of finite strain constitutive model for SMAs. Available yet still limited publications for SMAs model developed along this line can be obtained from M\"uller and Bruhns\cite{muller2006}, Teeriaho\cite{teeriaho2013} and Xu et al. \cite{xu2017}.

In this article, a three-dimensional constitutive model for SMAs considering large strains with large rotations is going to be proposed. This model utilizes the logarithmic strain as a finite strain measure for large deformation analysis so that its rate form hypoelastic constitutive relation can be consistently integrated to deliver a free energy based hyperelastic constitutive relation. The martensitic volume fraction and the second-order transformation strain tensor are chosen as the internal state variables to characterize the inelastic response exhibited by polycrystalline SMAs. Numerical experiments for basic geometries, such as a bar under tension and a torque tube under torsion are performed to test the capabilities of the newly proposed model.

\section*{PRELIMINARY} \label{Preliminary}
\subsection*{Continuum Mechanics}
Let body $ \mathcal{B} $ with its material point defined by a position vector $ \mathbf{X} $ in the reference (undeformed) configuration at time $ t_{0} $, let vector $ \mathbf{x} $ represent the position vector occupied by that material point in current (deformed) configuration at time $ t $, therefore the deformation process of the material point from its initial configuration to current configuration can be defined through the well known second order deformation gradient tensor $\mathbf{F}(\mathbf{x},t)$:
\begin{equation}\label{Deformation}
\mathbf{F}(\mathbf{x},t) =\frac{\partial \mathbf{x}}{ \partial \mathbf{X}}
\end{equation}
The velocity field of the material point can be defined by the second order tensor $\mathbf{v}$ as,
\begin{equation}\label{Velocity}
\mathbf{v} = \dfrac{d \mathbf x}{d t} = \dot{\mathbf x}
\end{equation}
Based on the velocity tensor $\mathbf{v}$, the velocity gradient $\mathbf{L}$ can be derived as,
\begin{equation}\label{eq:V_gradient}
\mathbf{L}= \frac{\partial \mathbf{v}}{ \partial \mathbf{x}}= \mathbf{\dot{F}}\mathbf{F} ^{-1}
\end{equation}
The following equation on polar decomposition of deformation gradient is well known,
\begin{equation}\label{eq:PolarDecom}
\mathbf{F  = UR = VR}
\end{equation}
In Eqn.(\ref{eq:PolarDecom}), the second order orthogonal tensor $\mathbf{R}$ is called the rotation tensor, i.e., $\mathbf{R}\mathbf{R^T}=\mathbf{R^T}\mathbf{R}=\mathbf{I}$, where $\mathbf{I} $ is second order identity tensor.  Symmetric and positive definite second order tensors $\mathbf{U}$ and $\mathbf{V}$ are called right (or Lagrangian) and left (or Eulerian) stretch tensors, through which the right Cauchy-Green tensor $\mathbf{C}$ and the left Cauchy-Green tensor $\mathbf{B}$ are obtained,
\begin{equation}\label{RCG}
\mathbf{C} = \mathbf{F^{T}F} =\mathbf{U}^2
\end{equation}
\begin{equation}\label{LCG}
\mathbf{b} = \mathbf{FF^{T}} =\mathbf{V}^2
\end{equation}
The logarithmic (or Hencky) strain of its Lagrangian type $ \mathbf{H} $ and Eulerian type $ \mathbf{h} $ are calculated as,
\begin{equation}\label{L_LogStrain}
\mathbf{H} = \frac{1}{2} \ln(\mathbf{ {C}}) =\mathbf{\ln ({U})}
\end{equation}
\begin{equation}\label{E_LogStrain}
\mathbf{h} = \frac{1}{2} \ln(\mathbf{ {b}}) =\mathbf{\ln ({V})}
\end{equation}
It is known velocity gradient $\mathbf{L}$ can be additively decomposed into a symmetric part called the rate of deformation tensor $\mathbf{D}$ plus an anti-symmetric part named spin tensor $\mathbf{W}$.
\begin{equation}\label{S_P_tensor}
\mathbf{L = D + W}, \qquad
\mathbf{D} =\dfrac{1}{2} \mathbf{(L+L^{T})}, \vspace{5pt}  \qquad
\mathbf{W} =\dfrac{1}{2} \mathbf{(L-L^{T})}
\end{equation}

\subsection*{Logarithmic Rate and Logarithmic Spin}\label{subsec:objective_rate}
As it was discussed in introduction, two commonly accepted kinematic assumption are usually considered in finite deformation theory. The first one is based on multiplicative decomposition of deformation gradient $\mathbf{F}$, and the other one is based on additive decomposition of total rate of deformation tensor $\mathbf{D}$. For a long period of time, rate form hypoelastic constitutive theory has been criticized for its failure to be exactly integrated to define an elastic material behavior\cite{simo2006}, this includes many well known objective rates such as Zaremba-Jaumann rate, Green-Naghdi rate and Truesdell rate etc.. Because of the aforementioned issues, many spurious dissipative phenomenons, such as shear stress oscillation and accumulated artificial residual stress are observed in even simple elastic material deformation. In other words, the non-integrable hypoelastic constitutive equation that uses objective rates is path-dependent and dissipative, and thus would deviate essentially from the recoverable elastic-like behavior \cite{xiao2006}.

As it was proved in the work by Xiao et al.\cite{xiao1997,xiao1997hypo,xiao2006}, Bruhns et al.\cite{bruhns1999self,bruhns2001large,bruhns2001self} and Meyers et al.\cite{meyers2003elastic,meyers2006choice}, the logarithmic rate of the logarithmic strain $\mathbf{h}$ of its Eulerian type is identical with the rate of deformation tensor $\mathbf{D}$, by which a grade-zero hypoelastic model can be exactly integrated into an finite deformation elastic model\cite{xiao1997}. This unique relationship between logarithmic strain $\mathbf{h}$ and the rate of deformation tensor $\mathbf{D}$ can be expressed as,
\begin{equation}\label{eq:Log_strain_rate}
\mathring{\mathbf{h}}^{log} = \dot{\mathbf{h}}+\mathbf{h} \bm{ \Omega}^{log}-\bm{ \Omega}^{log}\mathbf{h}= \mathbf{D}
\end{equation}
Where $ \bm{ \Omega}^{log} $ is called logarithmic spin introduced by Xiao and Bruhns\cite{xiao1997} with its explicit expression as:
\begin{equation}\label{eq:Log_spin}
\bm{\Omega}^{log} = \mathbf{W}+ \sum_{i \neq j}^{n}  \big(\frac{1+(\lambda_{i}/\lambda_{j})}{1-(\lambda_{i}/\lambda_{j})}+\frac{2}{\ln (\lambda_{i}/\lambda_{j})}\big) \mathbf{b}_i \mathbf{D} \mathbf{b}_j
\end{equation}
In which $\lambda_{i,j} (i,j=1,2,3) $ are the eigenvalues of Left Cauchy-Green tensor $ \mathbf{b} $ and $ \mathbf{b}_{i,j} $ are the corresponding subordinate eigenprojections. Given the antisymmetric logarithmic spin tensor, the associated second order rotation tensor $\mathbf{R}^{log}$ can be calculated through the following differential equation, and in most situations the initial condition can be assumed as $\mathbf{R}^{log}|_{t=0}= \mathbf I$.
\begin{equation}\label{eq:R_def}
{\bm{\Omega}^{log}}=\dot{\mathbf{R}}^{log}(\mathbf{R}^{log})^T
\end{equation}
Following the definition of corotational integration by Khan and Huang\cite{khan1995continuum}, applying the logarithmic corotational integration procedure on Eqn.(\ref{eq:Log_strain_rate}), assuming initial conditions $\mathbf{h}|_{t=0}= \mathbf 0$, yields the total logarithmic strain as follows,
\begin{equation}\label{eq:h-D}
\mathbf{h} = \int_{\text{coro.}}\mathbf{D} ~\text{d}t =(\mathbf{R}^{log})^T \bigg (\int \mathbf{R}^{log}\mathbf{D}^{e} (\mathbf{R}^{log})^T\text{d}t \bigg) \mathbf{R}^{log}
\end{equation}

\subsection*{Additive Decomposition of Logarithmic Strain }\label{AdditiveStrain}
Starting from the additive decomposition of the total rate of deformation tensor $\mathbf D$ into an elastic part $\mathbf{D}^{e}$ plus a transformation part $\mathbf{D}^{tr}$,
\begin{equation}\label{eq:add_D}
\mathbf{D}=\mathbf{D}^{e}+\mathbf{D}^{tr}
\end{equation}
By virtue of Eqn.(\ref{eq:Log_strain_rate}) , elastic part $\mathbf{D}^{e}$ and transformation part  $\mathbf{D}^{tr}$  in Eqn.(\ref{eq:add_D})  can be rewritten as the $\mathring{\mathbf{h}}^{e\_log}$ and $\mathring{\mathbf{h}}^{tr\_log}$ respectively,
\begin{equation}\label{eq:add_h_rate1}
\mathring{\mathbf{h}}^{e\_log}=\mathbf{D}^{e};~~\mathring{\mathbf{h}}^{tr\_log}=\mathbf{D}^{tr}
\end{equation}
Combine Eqn.(\ref{eq:add_D}) and Eqn.(\ref{eq:add_h_rate1}) , the following equation can be obtained.
\begin{equation}\label{eq:add_h_rate2}
\mathring{\mathbf{h}}^{log}=\mathring{\mathbf{h}}^{e\_log}+\mathring{\mathbf{h}}^{tr\_log}
\end{equation}
Similar as Eqn.(\ref{eq:h-D}), applying logarithmic corotational integration procedure on Eqn.(\ref{eq:add_h_rate2}) yields,
\begin{subequations}
	\begin{align}
	\mathbf{h}^{e}  = \int_{\text{corot.}}\mathbf{D}^{e} ~\text{d}t =(\mathbf{R}^{log})^T \bigg(\int \mathbf{R}^{log}\mathbf{D}^{e} (\mathbf{R}^{log})^T\text{d}t \bigg ) \mathbf{R}^{log}  \\
	\mathbf{h}^{tr} = \int_{\text{corot.}}\mathbf{D}^{tr} ~\text{d}t =(\mathbf{R}^{log})^T \bigg (\int \mathbf{R}^{log}\mathbf{D}^{tr} (\mathbf{R}^{log})^T\text{d}t \bigg ) \mathbf{R}^{log}
	\end{align}
\end{subequations}
Thus the following additive decomposition of total logarithmic strain can be received. Namely, the total logarithmic strain can be additively split into an elastic part plus a transformation part.
\begin{equation}\label{eq:add_h}
\mathbf{h}=\mathbf{h}^{e}+\mathbf{h}^{tr}
\end{equation}

\section*{MODEL FORMULATION}
\subsection*{Thermodynamic Potential of Constitutive Model}
In this section, the development for finite strain constitutive modeling of SMAs is going to be presented. This model formulation is based on the early established SMAs model by Lagoudas and coworkers \cite{boyd1996,lagoudas2012,lagoudas2008} within infinitesimal strain regime. We begin with an explicit expression for Gibbs free energy, in which Kirchhoff stress tensor $\bm{\uptau}$ and temperature $T$ are chosen as independent state variables for Gibbs free energy $G$. The martensitic volume fraction $ \xi $ and the second order transformation strain tensor $\mathbf{h}^{tr}$ are chosen as a set of internal state variables $ \bm{\Upsilon}=\{ \xi,\mathbf{h}^{tr}\} $ to capture the nonlinear response exhibited by polycrystalline SMAs. The explicit Gibbs free energy is given as:
\begin{equation}\label{eq:GIBBS_explicit}
\begin{aligned}
G=  -\dfrac{1}{2 \rho_{0}} \bm{\uptau} : \mathcal{S}\bm{\uptau} - \dfrac{1}{\rho_{0}}  \bm{\uptau} :[~\bm{\alpha}(T-T_0)+\mathbf{h}^{tr}]  +c \Big[(T-T_0)\\-T\ln (\dfrac{T}{T_0}) \Big] -s_0(T-T_0)+u_0+ \dfrac{1}{\rho_{0}}f(\xi)
\end{aligned}
\end{equation}
In which, $\mathcal{S}$ is the effective fourth-order compliance tensor calculated by using rule of mixtures defined in Eqn.(\ref{eq:S_mix}), $\mathcal{S}^A$ is compliance matrix for austenite phase, $\mathcal{S}^M$ is compliance matrix for martensite phase, and $\Delta\mathcal{S}$ is the phase difference between them. $ \bm{\alpha}$ is the second order thermoelastic expansion tensor, $ c $ is effective specific heat, $ s_0$ and $ u_0 $ are effective specific entropy and effective specific internal energy at reference state, respectively. Similar to the definition of effective compliance tensor $\mathcal{S}$ in Eqn.(\ref{eq:S_mix}), all those effective material parameters are using rule of mixture for their definition; $ T $ represents the temperature at current state while $ T_0 $ is temperature at reference state. $ f(\xi) $ is a smooth hardening function as it is introduced in original infinitesimal model.
\begin{subequations}
	\begin{align}\label{eq:S_mix}
	\mathcal{S}(\xi) &=\mathcal{S}^A + \xi(\mathcal{S}^M-\mathcal{S}^A)=\mathcal{S}^A + \xi\Delta\mathcal{S}  \\
	\bm{\alpha}(\xi) &=\bm{\alpha}^A + \xi(\bm{\alpha}^M-\bm{\alpha}^A)=\bm{\alpha}^A + \xi\Delta\bm{\alpha}  \\
	{c}(\xi)         &= c^A ~+ \xi(c^M-c^A)=c^A + \xi\Delta c  \\
	{s}_0(\xi)&= {s}_0^A + \xi({s}_0^M-{s}_0^A)={s}_0^A + \xi\Delta {s}_0\\\label{eq:u0}
	{u}_0(\xi)&= {u}_0^A + \xi({u}_0^M-{u}_0^A)={u}_0^A + \xi\Delta {u}_0
	\end{align}
\end{subequations}
Smooth hardening function $f(\xi)$ is defined in Eqn.(\ref{eq:Smooth_hardeing}) to consider the hardening effects associated with the transformation process. $a_1,a_2,a_3$ are introduced as intermediate material parameters in hardening function, and $n_1,n_2,n_3,n_4$ are curve fitting parameters to treat the smooth transition in the material response curve corner.
\begin{equation}\label{eq:Smooth_hardeing}
\begin{aligned}
f(\xi)=   \begin{cases} \cfrac{1}{2} a_1\Big(  \xi  + \frac{\xi^{n_1+1}} {n_1+1}+ \frac{(1-\xi)^{n_2+1}} {n_2+1} \Big)+a_3\xi ~, \; \dot{\xi}>0, \vspace{5pt} \\
\cfrac{1}{2} a_2\Big(  \xi  + \frac{\xi^{n_3+1}} {n_3+1}+ \frac{(1-\xi)^{n_4+1}} {n_4+1} \Big)-a_3\xi ~, \; \dot{\xi}<0 \end{cases}\\
\end{aligned}
\end{equation}
Following standard Coleman-Noll procedure, the constitutive relation between stress and strain is derived as,
\begin{equation}\label{eq:h_Cons_f}
\mathbf{h} = - \rho_{0}\frac{\partial G}{\partial \bm\uptau}=\mathcal{S}{\bm\uptau}+\bm\alpha(T-T_0)+ \mathbf{h}^{tr}
\end{equation}
Constitutive relation between entropy $s$ and temperature $T$ can also be derived as,
\begin{equation}\label{eq:entropy_Cons_f}
s =- \rho_{0}\frac{\partial G}{\partial T}=\dfrac{1}{\rho_{0}} \bm{\uptau}:\bm\alpha+c\ln (\dfrac{T}{T_0}) + s_0
\end{equation}
The strict form dissipation inequality can be rewritten in terms of internal state variables $ \bm{\Upsilon}=\{ \xi,\mathbf{h}^{tr}\} $ as:
\begin{equation}\label{eq:Dissipation_strict_V2}
-\rho_{0}  \frac{\partial G}{\partial \mathbf{h}^{tr}} :\mathring{\mathbf{h}}^{tr} -\rho_{0}  \frac{\partial G}{\partial \xi}\dot{\xi} \geqslant 0
\end{equation}
\subsection*{Evolution Equation of Internal State Variables}\label{sec:Evolution}
Evolution equations between internal state variables is going to be set up in this part. Following the same assumption from the early work of Lagoudas and coworkers \cite{boyd1996,lagoudas2008,lagoudas2012}, the following evolution relationship between $ \mathbf{h}^{tr} $ and $\xi$ is proposed. It is worth to point out that the rate adopted here is not a conventional time rate but logarithmic rate instead.
\begin{equation}\label{eq:Trans_Evol}
{\mathring{\mathbf h}}^{\textit{tr}}= \bm{\Lambda}  \dot{\xi},  \ \  \bm\Lambda=\begin{cases}\bm{\Lambda}^{\textit{fwd}}, \; \dot{\xi}>0, \vspace{5pt} \\ \bm{\Lambda}^{\textit{rev}}, \; ~\dot{\xi}<0, \end{cases}\\
\end{equation}
Where $\bm\Lambda^{\textit{fwd}}$ is called forward transformation direction tensor while $\bm\Lambda^{\textit{rec}}$ is called reverse transformation direction tensor. They are defined as follows respectively:
\begin{equation}\label{eq:direction}
\bm\Lambda^{\textit{fwd}}=
\frac{3}{2} H^{\textit{cur}}
\frac{\bm{\uptau}^{'}}{\bar{\uptau}^{'}},  \ \bm\Lambda^{rev}=
\frac{\mathbf h^{\textit{tr-r}}}{{\xi}^{\textit{r}}}.
\end{equation}
In Eqn.(\ref{eq:direction}), $ \bm{\uptau}^{'} $ is the deviatoric part of Kirchhoff stress tensor which is calculated by {\small $ \bm{\uptau}^{'} =\bm{\uptau} -{\small \frac{1}{3}}\textrm{tr}(\bm{\uptau})~\mathbf{I} $}, where $ \mathbf{I} $ is the second order identity tensor. The effective (von Mises equivalent) stress is given by $ \bar{\uptau}^{'} ={\small \sqrt{{{\small \frac{3}{2}}\bm\uptau}^{'}:\bm{\uptau}^{'}}}$. And $\mathbf h^{\textit{tr-r}}$ and ${\xi}^{r}$ represents the transformation strain value and martensitic volume fraction value at the starting point of reverse transformation. From experimental observation, the transformation strain is not a constant value but it usually depends on the material current stress state, thereby a current transformation strain $H^{\textit{cur}}$ is introduced through a exponential function dependent on current stress state in Eqn.(\ref{eq:Hcur}), where $H^{\textit{max}}$ is the maximum transformation strain and $\textit{k}_t$ is a curve fitting parameter, ${ \bar{\bm\uptau}}$ is effective stress of Kirchhoff stress.
\begin{equation}\label{eq:Hcur}
H^{\textit{cur}}(\bm\uptau)= H^{\textit{max}}(1-e^{-\textit{k}_t { \bar{\bm\uptau}}})
\end{equation}
\subsection*{Transformation Function}\label{Trans_Func}
After the definition of evolution equation for internal state variable, the next objective is to define a proper criterion to determine whether the transformation will happen or not. Substitute the evolution Eqn.(\ref{eq:Trans_Evol}) into the strict form dissipation inequality Eqn.(\ref{eq:Dissipation_strict_V2}), we obtain the following equation:
\begin{equation}\label{eq:Dissipation_xi}
(\bm\uptau:\bm\Lambda-\rho_{0}  \frac{\partial G}{\partial \xi})\dot{\xi}=\pi\dot{\xi}\geqslant 0
\end{equation}
Scalar variable $\pi$ is called general thermodynamic driving force conjugated to martensitic volume fraction $\xi$. Substitution of Gibbs free energy $G$ in Eqn.(\ref{eq:GIBBS_explicit}) into Eqn.(\ref{eq:Dissipation_xi}) yields the expression for $ \pi $:
\begin{equation}\label{eq:Driving_Force}
\begin{aligned}
\pi(\bm\uptau,T,\xi)=\bm\uptau:\bm\Lambda+
\dfrac{1}{2}\bm\uptau:{\Delta}\mathbf{S}:\bm\uptau+\bm\uptau:{\Delta}\mathbf{\alpha}(T-T_0)-\rho_0\Delta c
\big[ T-T_0\\ -T\ln(\dfrac{T}{T_0}) \big ] + \rho_0\Delta s_0 T - \rho_0\Delta u_0 - \frac{\partial f}{\partial \xi}
\end{aligned}
\end{equation}
Where material parameters $\Delta \mathcal{S},\Delta \mathbf{\alpha}, \Delta c, \Delta s_0, \Delta u_0 $ have the definition from Eqn.(\ref{eq:S_mix}) to Eqn.(\ref{eq:u0}). We assume that whenever the thermodynamic driving force $\pi$ reaches a critical value $Y $ ($ -Y $), the forward (reverse) phase transformation will take place. Therefore, a transformation function $\Phi$, defined as Eqn.(\ref{eq:Transfor_Fun}), can be used as a criteria to determine the occurrence for phase transformation.
\begin{equation}\label{eq:Transfor_Fun}
\normalfont{\Phi}=\begin{cases}~~\pi - Y, \; \dot{\xi}>0, \vspace{5pt} \\ -\pi - Y, \; \dot{\xi}<0, \end{cases}\\
\end{equation}
In the continuous development of Lagoudas et al.\cite{lagoudas2012} model, a stress dependent critical value $Y$ was proposed. A constant reference value $Y_0$ and an additional parameter D are introduced into $Y$ such that it can better capture the smooth transition during transformation initial zone. Critical value $Y$ is defined as follows,
\begin{equation}\label{Critical_Y}
Y(\bm{\uptau}) = \begin{cases}Y_0 + D\bm\uptau:\bm\Lambda^{\textit{fwd}}, \; \dot{\xi}>0, \vspace{5pt} \\ Y_0 + D\bm\uptau:\bm\Lambda^{\textit{rev}}, \; \dot{\xi}<0, \end{cases}\\
\end{equation}
To be satisfied with the principle of maximum dissipation, a so-called Kuhn-Tucker constraint conditions has also been placed on the evolution equation for internal state variables, which are expressed as follows for forward and reverse transformation cases respectively:
\begin{equation}\label{eq:Kuhn-Tucker}
\begin{aligned}
\dot{\xi} \geqslant 0; \quad \Phi(\bm\uptau,T,\xi)= ~~\pi - Y \leqslant 0;  \quad  \Phi\dot{\xi}=0;~~~\bf{(A\Rightarrow M)}\\
\dot{\xi} \leqslant 0; \quad \Phi(\bm\uptau,T,\xi)= -\pi - Y \leqslant 0; \quad   \Phi\dot{\xi}=0;~~~ \bf{(M\Rightarrow A)}
\end{aligned}
\end{equation}
\section*{Consistent Tangent Stiffness and Thermal Matrix}\label{sec:Jacobian}
In this section, a detailed derivation of consistent tangent stiffness matrix and thermal matrix is provided to complete the proposed model. In most typical displacement-based commercial finite element software, like Abaqus, when an user defined material subroutine (UMAT) is written, consistent tangent matrices are usually required from finite element program solver to achieve a fast and accurate solution for global equilibrium equations during Newton-Raphson iteration procedure. Normally, consistent tangent matrices can be expressed in a rate form as defined in Eqn.(\ref{eq:Jacobian}), $\mathcal{L}$ is consistent tangent stiffness matrix and $\Theta$ is consistent thermal matrix.
\begin{equation}\label{eq:Jacobian}
\mathring{\bm{\uptau}}  =  {\mathcal{L}}\mathring{\mathbf h}
+ \Theta \dot T
\end{equation}
Apply logarithmic rate on constitutive stress strain Eqn.(\ref{eq:h_Cons_f}), where $\mathcal{C}$ is the stiffness matrix, the inverse of compliance tensor $\mathcal{S}$
\begin{equation}\label{eq:rate_cons}
\mathring{\bm{\uptau}}  = {\mathcal{C}}~[\mathring {\mathbf h}  -  \bm\alpha\dot T - ({\Delta\mathcal{S}}\bm{\uptau} +  \Delta{\bm\alpha}(T-T_0) + \bm\Lambda )\dot \xi~]
\end{equation}
Take chain rule differentiation on transformation function Eqn.(\ref{eq:Transfor_Fun}), and replace conventional time rate with logarithmic rate. Be noticed that logarithmic rate is equivalent to conventional rate when it is applied on a scalar.
\begin{equation}\label{eq:rate_TransFun}
\dot{\Phi}  = \partial_{\bm{\uptau}}\Phi:\mathring{\bm\uptau} + \partial_{T}\Phi\dot{T} + \partial_{\xi}\Phi\dot{\xi} = 0
\end{equation}
Substitute Eqn.(\ref{eq:rate_cons}) back into Eqn.(\ref{eq:rate_TransFun}) to eliminate $\mathring{\bm{\uptau}}$ and solve it for $\dot \xi$, the following expression for $\dot \xi$ can be obtained,
\begin{equation}\label{eq:rate_xi}
\dot{\xi}  = -\dfrac{\partial_{\bm\uptau}\Phi: \mathcal{C} \mathring {\mathbf h} +(\partial_{T}\Phi- \partial_{\bm\uptau}\Phi: \mathcal{C} \bm \alpha)\dot T}{\partial_{\xi}\Phi- \partial_{\bm\uptau}\Phi: \mathcal{C} (\Delta\bm S\bm\uptau+\bm\Lambda+\bm)}
\end{equation}
Substitute Eqn.(\ref{eq:rate_xi}) back into rate form constitutive Eqn.(\ref{eq:rate_cons}), eliminate $\dot \xi$ and after some tensorial manipulations, a final explicit expression corresponding to Eqn.(\ref{eq:Jacobian}) can be expressed as follows,
\begin{equation}\label{eq:}
\begin{aligned}
\mathring{\bm{\uptau}}  = \Big[ \mathcal{C}+\dfrac{[\mathcal{C}({\Delta\mathcal{S}}\bm{\uptau}+ \bm\Lambda )] \otimes  [\mathcal{C} \partial_{\bm\uptau}\Phi]}{\partial_{\xi}\Phi- \partial_{\bm\uptau}\Phi: \mathcal{C}(\Delta\mathcal{S}\bm\uptau+\bm\Lambda)} \Big] \dot{\bm\varepsilon}
+  \Big[
- \mathcal{C}\bm\alpha \\+
\dfrac{ \mathcal{C}({\Delta\mathcal{S}}\bm{\uptau}+ \bm\Lambda)  (\partial_{T}\Phi - \partial_{\bm\uptau}\Phi: \mathcal{C}\bm\alpha )}
{\partial_{\xi}\Phi- \partial_{\bm\uptau}\Phi: \mathcal{C}(\Delta\mathcal{S}\bm\uptau+\bm\Lambda)}
\Big] \dot T
\end{aligned}
\end{equation}
In which consistent tangent stiffness matrix ${\mathcal{L}}$ is obtained as,
\begin{equation}
{\mathcal{L}}=\mathcal{C}+\dfrac{[\mathcal{C}({\Delta\mathcal{S}}\bm{\uptau}+ \bm\Lambda ] \otimes  [\mathcal{C} \partial_{\bm\uptau}\Phi]}{\partial_{\xi}\Phi- \partial_{\bm\uptau}\Phi: \mathcal{C}(\Delta\mathcal{S}\bm\uptau+\bm\Lambda)}
\end{equation}
and consistent thermal matrix $\Theta$ is derived as,
\begin{equation}
\Theta =
- \mathcal{C}\bm\alpha +
\dfrac{ \mathcal{C}({\Delta\mathcal{S}}\bm{\uptau}+ \bm\Lambda )  (\partial_{T}\Phi - \partial_{\bm\uptau}\Phi: \mathcal{C}\bm\alpha )}
{\partial_{\xi}\Phi- \partial_{\bm\uptau}\Phi: \mathcal{C}(\Delta\mathcal{S}\bm\uptau+\bm\Lambda)}
\end{equation}

\section*{NUMERICAL RESULTS}\label{Result}
In this section, Boundary value problems, including a simple extension problem for SMA bar and a shear problem for a SMA torque tube,  will be investigated to test the capabilities of proposed finite strain model, the response predicated by which is going to be compared with its infinitesimal counterpart. Besides, the cyclic pseudoelastic response of the SMA torque tube is also going to be examined to evaluate the effects of artificial residual stress introduced by objective rates.

\subsection*{Bar Problem}\label{subsec:bar}
The first boundary value problem analyzed is a SMA bar experiencing stress-induced phase transformation under external pressure at constant temperature, which is typically called a pseudoelastic (or superelastic) response exhibited by SMAs. Referring to Fig.\ref{fig:Bar_Schematic} for problem schematic, a long SMA bar with length  $L=100$ unit (mm) and has a square cross section with edge length $ a=10 $ unit (mm). Mechanical boundary conditions are left face fixed in certain lines and points to remove rigid body motions and right face is free to move but with an applied external pressure in its length direction. The material parameters used in this simulation are summarized in Tab.\ref{tab:MaterialProperty_bar} referenced from literature \cite{lagoudas2008}.

\begin{figure*}[t!]
	\centering
	\includegraphics[width=0.6\textwidth]{figures/Bar_Schematic.jpg}
	\caption{\uppercase{Schematic of a SMA bar extension problem under external pressure at constant temperature}}
	\label{fig:Bar_Schematic}
	\vspace{0.5cm}
\end{figure*}

The loading history of SMA bar is the following: increase the pressure on right face from zero value to a maximum value 1200 (MPa), during which the SMA bar will experience a stress-induced extension due to forward transformation from austenite phase to detwinned martensite phase; Decrease the pressure linearly from its maximum value to zero, during which the SMA bar will contract to its original length due to the reverse transformation from detwinned martensite phase to austenite phase. The temperature is kept constant as $360$K throughout the whole loading procedure. The material response predicted by proposed finite strain model are compared against its infinitesimal counterpart.

\begin{table*}[h!]
	\centering
	\caption{SUMMARY OF USED MATERIAL PARAMETERS FOR NUMERICAL  SIMULATIONS}
	\renewcommand{\arraystretch}{0.8}
	\begin{tabular}{c|lr|ll} \toprule
		Type                         &Parameter                        & Value                                   &Parameter            & Value  \\                                       \midrule
		&$E_A$                            & 90   [GPa]                              & $C_A$                & 16  [MPa/K]\\
		&$E_M$                            & 63   [GPa]                              & $C_M$               & 10  [MPa/K]\\
		Material Constants       &$\nu_A=\nu_M$                          & 0.3~~~~~~~~                              & $M_s$                & 308  [K]\\
		10                      &$\alpha_A=\alpha_M$    &    2.2$\times$10$^{-5}$ [K$^{-1}$]                           & $M_f$                &242  [K]\\
		&                       &           & $A_s$                 &288  [K]\\
		&                       &       & $A_f $                 & 342  [K]\\                                   \midrule

		&$ H^\textit{max}$               & 1\%, 3\%, 5\%, 10\%                     & $n_1$              & 0.5 \\
		Smooth Hardening         & $k_t$                          &0.0075                              & $n_2$         & 0.5 \\
		6                               &              &                     & $n_3$         &  0.5\\
		& & & $n_4$     &  0.5           \\
		\bottomrule
	\end{tabular}
	\label{tab:MaterialProperty_bar}
\end{table*}
\begin{figure}[t]
	\centering\hspace*{-1cm}
	\includegraphics[width=0.5\textwidth]{figures/Bar_COM_H01_M2.pdf}\vspace{-0.3cm}
	\caption{\uppercase{Comparison of pseudoelastic response for a SMA bar predicted by  proposed finite strain model and infinitesimal strain model with transformation strain} ${H}^{max}=1\%$ }
	\label{fig:Bar_H01}
\end{figure}
\begin{figure}[t]
	\centering\hspace*{-1cm}
	\includegraphics[width=0.5\textwidth]{figures/Bar_COM_H03_M2.pdf}\vspace{-0.3cm}
	\caption{\uppercase {Comparison of pseudoelastic response for a SMA bar predicted by  proposed finite strain model and infinitesimal strain model with transformation strain} ${H}^{max}=3\%$ }
	\label{fig:Bar_H03}
\end{figure}
\begin{figure}[t]
	\centering\hspace*{-1cm}
	\includegraphics[width=0.5\textwidth]{figures/Bar_COM_H05_M2.pdf}\vspace{-0.3cm}
	\caption{\uppercase {Comparison of pseudoelastic response for a SMA bar predicted by  proposed finite strain model and infinitesimal strain model with transformation strain} ${H}^{max}=5\%$ }
	\label{fig:Bar_H05}
\end{figure}
\begin{figure}[t]
	\centering\hspace*{-1cm}
	\includegraphics[width=0.5\textwidth]{figures/Bar_COM_H10_M2.pdf}\vspace{-0.3cm}
	\caption{\uppercase {Comparison of pseudoelastic response for a SMA bar predicted by  proposed finite strain model and infinitesimal strain model with transformation strain} ${H}^{max}=10\%$ }
	\label{fig:Bar_H10}
\end{figure}
As the result is shown in Fig..\ref{fig:Bar_H01}, when the maximum transformation is strain $1\%$, the difference of pseudoelastic response curve predicted by the two models is almost negligible. However, with the increasing of maximum transformation strain from $1\%$ to $3\%$, and more to $5\%$ and $10\%$, the difference of predicted pseudoelastic response is becoming predominant. Specifically, with max transformation strain $H^{max}=3\%$ in Fig.\ref{fig:Bar_H03}, the difference is becoming perceivable at the end of forward transformation, normalized displacement has larger value predicted by proposed finite strain model in contrast to infinitesimal strain model. This response difference is growing substantial in the cases of $H^{max}$ to be $5\%$ and $10\%$. Since there is no rotation involved here, the difference for the result comes from the fact that infinitesimal strain neglect the higher order terms in strain measure while logarithmic strain used in proposed model doesn't.
\subsection*{Tube Problem}\label{sec:torque_tube}
In this section, a shear problem of a hollow cylindrical SMA torque tube under torsion loading at constant temperature is studied. Referring to Fig.\ref{fig:Tube_Schematic} for problem schematic, a full size geometry of long hollow cylindrical torque tube is depicted in Fig.\ref{fig:Tube_Schematic}(a). In order to reduce the computational cost, only one small segment tube with length $L$ and inner radius $r$ is chosen for analysis. The segment tube has a geometry ratio of $L/r =2$.

\begin{figure*}[t]
	\centering
	\includegraphics[width=0.8\textwidth]{figures/TorsionTubeSchematic.pdf}\vspace{-1.8cm}
	\caption{\uppercase{Schematic for the shear problem of hollow cylindrical SMA torque tube} }{\vspace{-0.2cm}}
	\label{fig:Tube_Schematic}
\end{figure*}
As it is shown in Fig.\ref{fig:Tube_Schematic}(b), the mechanical boundary condition is following: the tube left face is fixed in all degrees of freedom while the right face is subject to a torsion loading through a twist angle $\theta_z(t)$ along its longitudinal direction. The loading history is: the twist angle $\theta_z(t)$ increases proportionally from zero to a maximum value at $t = 0.5$, during which the torque tube undergoes a fully forward phase transformation from austenite phase to detwinned martensite phase. Afterwards, twist angle $\theta_z(t)$ proportionally decreases from its peak value to zero, during which the SMA tube experienced a reverse phase transformation from martenite phase to austenite phase. Temperature is kept as a constant value of $360$ K throughout this whole loading process. Material parameters used in this numerical experiment are choosing from Tab.\ref{tab:MaterialProperty_bar}.

\begin{figure}[t]
	\vspace{-0.5cm}\centering\hspace*{-0.8cm}
	\includegraphics[width=0.5\textwidth]{figures/Tube_COM_L6_H01.pdf}\vspace{-0.5cm}
	\caption{\uppercase{Comparison of pseudoelastic response for a short SMA torsion tube predicted by proposed finite strain and infinitesimal strain model with transformation strain} ${H}^{max}=1\%$, \uppercase{geometry ratio} $L/r=2$  }
	\label{fig:Tube_L6_H01}
\end{figure}
\begin{figure}[t]
	\vspace{-0.5cm}\centering\hspace*{-0.8cm}
	\includegraphics[width=0.5\textwidth]{figures/Tube_COM_L6_H03.pdf}\vspace{-0.5cm}
	\caption{\uppercase{Comparison of pseudoelastic response for a short SMA torsion tube predicted by proposed finite strain and infinitesimal strain model with transformation strain} ${H}^{max}=3\%$, \uppercase{geometry ratio} $L/r=2$  }
	\label{fig:Tube_L6_H03}
\end{figure}
\begin{figure}[t]
	\vspace{-0.5cm}\centering\hspace*{-0.8cm}
	\includegraphics[width=0.5\textwidth]{figures/Tube_COM_L6_H05.pdf}\vspace{-0.5cm}
	\caption{\uppercase{Comparison of pseudoelastic response for a short SMA torsion tube predicted by proposed finite strain and infinitesimal strain model with transformation strain} ${H}^{max}=5\%$, \uppercase{geometry ratio} $L/r=2$  }
	\label{fig:Tube_L6_H05}
\end{figure}
\begin{figure}[t]
	\vspace{-0.5cm}\centering\hspace*{-0.8cm}
	\includegraphics[width=0.5\textwidth]{figures/Tube_COM_L6_H10.pdf}\vspace{-0.5cm}
	\caption{\uppercase{Comparison of pseudoelastic response for a short SMA torsion tube predicted by proposed finite strain and infinitesimal strain model with transformation strain} ${H}^{max}=10\%$, \uppercase{geometry ratio} $L/r=2$  }
	\label{fig:Tube_L6_H10}\vspace{-0.5cm}
\end{figure}
It can be observed from the results showing from Fig.\ref{fig:Tube_L6_H01} to Fig.\ref{fig:Tube_L6_H10}, although there is no considerable difference on the material response predicted by both models for maximum transformation strain $H^{max}= 1\% \sim 3\% $, perceivable difference for maximum transformation strain $H^{max}= 5\% $ is showing in Fig.\ref{fig:Tube_L6_H05}, and this difference continues to grow substantially as maximum transformation strain increases to $H^{max}= 10\% $ in Fig.\ref{fig:Tube_L6_H10}. Through the above comparison on the pseudoelastic response for segment torque tube, it is demonstrated that, under large rotations, the difference of predicted material response by proposed finite strain model and infinitesimal model will be perceivable within moderate strain regime of $5\%$, and it continues to grow substantially in large strain regime at $10\%$.

\section*{Cyclic Response of SMA Torque Tube }
As it was discussed in the section of introduction, based on the additive decomposition in finite deformation theory, a rate form hypoelastic constitutive equation is often seen as stress and strain relationship, in which a objective rate is  usually required on the stress tensor in order to meet the principle of objectivity. There are many different objective rates proposed by different researchers along this line, among which several famous ones are Zaremba-Jaumann rate, Green-Naghdi rate and Truesdell rate etc.. However, for a long period of time, rate form hypoelastic constitutive theory has been criticized for its inconsistent choices on objective rates\cite{simo2006}, and also the rate form hypoelastic constitutive equation is not able to be integrated to deliver a algebraic constitutive equation, thereby many spurious phenomenons, such as shear stress oscillation, dissipative phenomenon or artificial residual stress are observed in even simple elastic deformation.
The aforementioned self-inconsistent issues of hypoelastic constitutive model are resolved by the logarithmic rate proposed by Xiao et al. \cite{xiao1997,xiao1997hypo,xiao2006}, Bruhns et al.\cite{bruhns1999self,bruhns2001large,bruhns2001self}, Meyers et al.\cite{meyers2003elastic,meyers2006choice}.

In this section, a segment torsion tube is analyzed by proposed finite strain model and its original infinitesimal counterpart with Abaqus NLGEOM (nonlinear geometry) option to extend it for large deformation analysis. The loading conditions and material parameters used are the same as previous segment torsion tube. It should be clear, when the Abaqus NLGEOM option is activated for infinitesimal strain based SMA model during implicit analysis, the strain measure is logarithmic strain and Jaumman rate is the utilized objective rate to capture rotation deformation. As it is mentioned about with objective rates, artificial residual stresses will be introduced by using other objective rates except for the logarithmic one.

Pseudoelastic response of the SMA torque tube are examined by proposed finite strain model and its infinitesimal counterpart with Abaqus NLGEOM option. At the end of the first loading cycle, the Von Mises stress are checked in both cases. As it is shown in Fig.\ref{fig:Residual_tube}, the artificial residual stress is almost zero predicted by proposed finite strain model, while the residual stress obtained from infinitesimal model with Abaqus NLGEOM option is around 8 MPa in contrast. The artificial residual stresses from those two cases are summarized in principal components representation at Tab.\ref{table:T_ReStress}.
\begin{figure*}[t!]
	\centering\vspace{-0.2cm}
	\includegraphics[width=0.8\textwidth]{figures/ModelResultsComparison.pdf}\vspace{-1.3cm}
	\caption{\uppercase{Comparison of artificial residual stress contour predicted by proposed finite strain model and infinitesimal model  with Abaqus NLGEOM option for a SMA torque tube after one loading cycle.}}
	\label{fig:Residual_tube}
\end{figure*}
\begin{table*}[h!]
	\centering\vspace{0.5cm}
	\caption{\uppercase{Artificial residual stress introduced for SMA torque tube after one loading cycle}}
	\label{table:T_ReStress}
	\begin{tabular}{@{}lcccc@{}}
		\toprule
		&{Stress Components}          &{Proposed finite strain model}  & \pbox{30cm}{Infinitesimal strain model with\\ Abaqus NLGEOM} &\\ \midrule
		&Principal Max.(MPa) &1.77e-7        & 4.04           &\\
		&Principal Mid.(MPa) &1.05e-7        & -4.19          &\\
		&Principal Min.(MPa) &3.22e-8        &-4.32           &\\
		\bottomrule
	\end{tabular}
\end{table*}

Build on the results for one loading cycle, let us now examine whether this accumulation of artificial residual stresses will continue to grow, and how it will affect the material response of SMAs torque tube under cyclic loadings. Referring to Fig.\ref{fig:Tube_ABA_90} for material response predicted by the infinitesimal model using Abaqus NLGEOM option, it can be seen that there is a clear response shifting from initial to final loading cycle due to the accumulation of artificial residual stress. Specifically, the stress levels required to start the forward phase transformation is decreasing, maximum shear stress achieved is increasing and the shear stress at end of each loading cycle is deviating more and more from the initial zero value. In contrast, material response predicted by proposed finite strain model in Fig.\ref{fig:Tube_LEI_90}, the initial material response is nearly overlapping with the material response from subsequent loading cycles.
\begin{figure}[t]
	\vspace{-0.5cm}
	\centering\hspace*{-0.8cm}
	\includegraphics[width=0.5\textwidth]{figures/Torque_Tube_ABA_90Cycles.pdf}\vspace{-0.7cm}
	\caption{\uppercase{Cyclic pseudoelastic response of a SMA torque tube predicted by infinitesimal model with Abaqus NLGEOM option under 90 cyclic loadings}}
	\label{fig:Tube_ABA_90}
\end{figure}
\begin{figure}[t]
	\vspace{-0.5cm}
	\centering\hspace*{-0.8cm}
	\includegraphics[width=0.5\textwidth]{figures/Torque_Tube_LEI_90Cycles.pdf}\vspace{-0.7cm}
	\caption{\uppercase{Cyclic Pseudoelastic response of a SMA torque tube predicted by proposed finite strain model under 90 cyclic loadings}}
	\label{fig:Tube_LEI_90}
\end{figure}

Based on the results for segment SMA torque tube under cyclic loading, it is demonstrated that, because of the small amount of artificial residual stress introduced by using Abaqus NLGEOM option, the infinitesimal strain based constitutive model for SMAs will predict an shifting, instead of stable, cyclic pseudoelastic response for a torque tube. It is also shown that the proposed finite strain SMA constitutive model, based on logarithmic strain and logarithmic rate, can effectively rule out the effects of artificial residual stress during cyclic loadings. Nevertheless, it is worthy of pointing out for general metallic material within small strain regime during low loading cycles, the amount of artificial residual stresses have quite limited effects on the material response, and it is still a practical and relatively accurate way to utilize the Abaqus NLGEOM option to consider deformation involved with large rotations. At the same time, it is crucial to realized that such undesired artificial stresses need be taken into consideration when the material is undergoing a large number of cyclic loadings, for which a finite strain constitutive model for SMAs based on logarithmic strain and logarithmic rate is indispensible in order to deliver an stable and accurate material response.
\section*{CONCLUSION}\label{Conc}
Based on the infinitesimal strain based constitutive model for shape memory alloys from Lagoudas and coworkers\cite{boyd1996,lagoudas2012}, a three dimensional phenomenological constitutive model for martensitic transformation in polycrystalline shape memory alloys considering large strains and large rotations is proposed in this work. Numerical simulations considering basic SMA component geometries, such as a bar and a torque tube under stress induced phase transformation, are performed to test the capabilities of the proposed model. For numerical examples of SMA bar, relatively large discrepancies are observed between the responses predicted by the proposed model and its infinitesimal counterpart when strain is no longer considered small. In the numerical simulations of a SMA torque tube with large rotations, it is demonstrated that the difference of predicted material response will be perceivable in moderate strain regime of $5\%$ and continues to grow substantially in large strain regime at $10\%$.  From the results of SMA torque tube under cyclic loading, it has been shown that infinitesimal strain based constitutive model will predict an shifting cyclic pseudoelastic response as a result of the artificial residual stress introduced by using Abaqus NLGEOM option. In comparison, the proposed finite strain SMA constitutive model, based on logarithmic strain and logarithmic rate, can effectively rule out the effects of artificial residual stress during cyclic loadings.

\section*{Acknowledgments}\label{Ack}
The author would like to acknowledge the financial support provided by the Qatar National Research Fund under the grant number: NPRP 7-032-2-016, and the NASA University Leadership Initiative project under the grant number: NNX17AJ96A.

\bibliographystyle{asmems4}

redpajama_set_name: RedPajamaArXiv


text:
Bread and cereals hit by shrinkflation
posted by Andrew Allen
in Procurement
Cereals and bread are the food categories that have been hit most by shrinkflation, according to a report.
The Office for National Statistics (ONS) found 206 products in all categories had shrunk in size, while 79 increased, when it studied the price of 17,000 items between September 2015 and June 2017.
And while it may have been expected that the fall in the value of the pound sparked by the Brexit vote would lead to more shrinkflation, due to a rise in the price of imported materials, this did not occur.
"There was no trend in the frequency of size changes over this period, which included the EU referendum," the ONS said.
The ONS found 36 cases of shrinkflation among bread and cereals. The next two categories with the largest number of shrinkflation cases were meat and confectionary.
Food categories with most product size changes included bread and cereals, meat, and sugar, jam, syrups, chocolate and confectionery.
The non-food categories with the most size increases and reductions were appliances, personal care products such as toilet rolls, nappies and tissues, and non-durable household goods such as kitchen roll and washing-up liquid.
Among the treats found to have shrunk substantially since 2012 are Toblerone, Terry's Chocolate Orange and Maltesers. Makers have blamed the shrinkage on higher cocoa prices.
But the ONS said, contrary to popular opinion, shrinkflation was not widespread.
"Overall, [such products] represented a small minority of products in our sample," said the report.
However, the ONS also stressed that for the purpose of measuring inflation it targets high-expenditure, easy-to-follow products.
"As a result, the size changes in our sample will not necessarily be representative of the changes occurring in the market as a whole," it said.
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redpajama_set_name: RedPajamaCommonCrawl


Sophie Habib Gorgi - born in Cairo in 1922. The daughter of Habib Gorgi, a water colours painter and a pedagogue whose theories changed art education in Egypt, she was encouraged to join the Art institute, from which she graduated in 1946 and became an art teacher. In addition to her work in education, she was very active in social work and founded a club in a poor district in Cairo where children could play sports, learn art and acquire working skills.
In 1948 Sophie married Ramses Wissa Wassef, whom had started his experiment in creative weaving in an old Cairo school in 1942.
She had her two daughters, Suzanne (1950) and Yoanna (1952).
The couple bought a piece of land in the Harrania village where they started the Art Center. At the beginning Sophie was involved in the social and educational aspect of the Center and in 1969 she set up a canteen for the weavers where she taught them how to prepare healthy food for their children. After the sudden death of Ramses in 1974 she took charge of group of artist that Ramses had started. They are known as the first generation wool weavers.
In 1989 Sophie built a museum for the private tapestry collection which demonstrates the progress of the weavings since 1944 till today. The collection contains Ramses' work as well as her own.
Sophie is an accomplished water colours painter; her works have been exhibited in several art galleries in Cairo.
Sophie is an expert on natural vegetable dyes for wool.
"What gave me the strength to continue is my love for Ramses and my belief in everything he said."


This document is for selling or buying an entire company. It is an extremely authoritative document which can be used for high value transactions and for any sort of business.
You may be interested in a document to sell an entire company documents or alternatively, business sale agreements.
150 warranties sounds an awful lot. Do you really need them? Will you understand them? Net Lawman advises: absolutely yes and absolutely yes! Our warranties are written in plain English. A seller should start with a full set unless he is sure he knows everything there is to know about his proposed acquisition, or the value is very small, or the company is not trading.


text:
.. _bokeh.models.glyphs.Patches:

bokeh.models.glyphs.Patches
---------------------------

.. autoclass:: bokeh.models.glyphs.Patches
    :members:
    :inherited-members:

redpajama_set_name: RedPajamaGithub


Thanks for sharing this Mark.
Thanks for your ideas Mark. These are all great ideas, but even the smaller resources can sometimes help bring traffic. I've used sites like State of the art mailer, List Joe, etc. Sites like that are safelists and they can help along with the other many available resources. One thing I've learned about getting traffic to a website is there's never enough, and I believe no matter how much you have to spend or where you advertise, the more resources you put to use, the better. You never know just where your best prospects will be. It's like tossing out that line and waiting for the bite. It's unexpected when or where it will happen. That's my opinion when it comes to bringing traffic to a website. I use as many resources I can and the help of advice like yours. It goes back to the quote, " The sky is the limit.
I Love the work you have put into it Mark on how to get traffic to your site, I know doing the right SEO is the Most important thing to do. and blogging does help a lot. I have made a blog with a post on it and I put everything on it that I can to drive people to my site.


Over 175,000 of Europe's bells were confiscated by the Nazis during World War II. A communal musical instrument, bells have permeated secular and religious life for centuries. Artistic, musical, and historical works, bells are bound up in the fabric of their nations, regions, and cities as cultural property and heritage, reflecting civic, social, and religious traditions as well as customs of bell founding and performance. Unlike the aesthetic motives that fueled Nazi-era looting of other musical material culture, bells were taken for their metal content for use in the Reich war machine, even though international law prohibited such seizures and destruction. By the war's end, an estimated 150,000 bells were destroyed, leaving a sonic gap in the European landscape. Bells that remained were repatriated to their countries of origin. Bell losses were remembered at the International Military Tribunal at Nuremberg and remain symbols of community and culture, war and peace.
Carla Shapreau is a Senior Fellow in the Institute of European Studies, a Curator in the Department of Music, and a Lecturer in the School of Law at the University of California, Berkeley. Co-author of the Ferrell-Vogüé Machaut Manuscript, Oxford: DIAMM Publications, 2014 (American Musicological Society Claude V. Palisca Award 2015) and Violin Fraud -- Deception, Forgery, Theft and Lawsuits in England and America, Oxford University Press, 1998, she has written broadly regarding issues of musical cultural property. Carla Shapreau also is a violin maker.


Show the brave individuals of the Army some support with Army Stickers! Each sheet features tanks, dog tags, boots, and more, in natural green and black colors. Use them in scrapbooks, surprise soldier homecomings, and as gifts!
Length: 7/8" - 1 1/2"
Package contains 24 acid-free stickers.


The NEW PANDORA Sterling Silver Barrel Clasp Charm Bangle has an inspirational style for you to create and design your own truly stylish bracelet, marking special moments in your life or just to reveal your creativity. The ever growing collection of beads and charms thread right onto the bangle, and are hand crafted and designed to remind you of those moments you never want to forget. The bangle fastens with a barrel locking clip clasp which also disguises as an extra bead. Start creating your unique bracelet now and pride yourself on the fact that no two bracelets are the same. Wear it plain or filled with beads, on its own or stacked with other bracelets from the PANDORA collection, no matter what your style it is sure to be a favourite accessory you can't be without! A PANDORA bracelet makes an on-going perfect gift as there is a charm that fits every occasion, so for years to come, whether it be a birthday, wedding, graduation or just simply to say I love you, there is a charm available for you. You can now add clips to your PANDORA Leather Bracelet and the new Bangle to create sections and restrict the movement of your charms by adding a C-Shaped Silicone Insert underneath your clip. Please request these in the 'Additional Information' field at checkout when buying a clip by typing P1110 or Silicone Insert.


text:
Russian commandos to get Mi-8AMTSh-VN helicopter in 2020
Leonardo Falco Xplorer drone completes first flight
No cold-weather tests and fly-off among candidates for Canadian new fighter jet
Will future UAVs fly like a bird ?
World Aviation Defense & Security News - China
Chinese Y-20 strategic transport aircraft to enter service in People's Liberation Army in two years
The Y-20, China's first domestically designed large transport aircraft developed by Xi'an Aircraft Industrial Corporation, is likely to enter service with the People's Liberation Army in the next two years, Chinese newspaper People's Daily reported on Oct. 16.
Xi'an Aircraft Industrial Corporation Y-20 "Kunpeng" large military transport aircraft
The Chinese Communist Party said the Y-20 will be shown to the public for the first time at the Zhuhai Airshow in Guangdong province next month. The plane makes China the fourth nation in the world with the ability to develop 200-ton transport aircraft after the United States, Russia and Ukraine, the paper said.
The Y-20 is a landmark in Chinese aviation history as the aircraft is a brand new design, the report said, since unlike older transport aircraft such as the Y-7 and Y-8, which were based on Russian models, the Y-20 is an entirely Chinese design. People's Daily said Xi'an Aircraft Industrial Corporation has gained experience through developing fighters and bombers from the 1990s.
Defense Aviation and Aerospace Air Force Show Daily News
Farnborough Airshow 2020
Air Show China 2020


text:
Engineers conduct test of rocket engine powered by plastic waste
Credit: Pixabay/CC0 Public Domain
A team of engineers with Pulsar Fusion has conducted a ground test of its plastic-waste-powered rocket engine at the UK's Ministry of Defence military base in Salisbury last week. The team has posted a video of the test on YouTube.
Pulsar Fusion is a U.K.-based company established to find a way to make use of nuclear fusion as a power source, both for producing electricity and pushing rockets through space. The company has set a goal of developing and deploying a nuclear fusion rocket engine by 2025—one that could send a rocket to Mars in half the time of current technology. In the meantime, the company has set its sights on developing a rocket engine powered by plastic waste products.
In speaking with the press, officials with Pulsar referred to their project as a "green" rocket. It uses a hybrid fuel made by mixing polyethylene with a nitrous oxide oxidizer. The result is fed into a combustion chamber where it is held under pressure until fired. They note that the plastic they are using is a type that is commonly used in a wide variety of products, such as cutting boards and piping, which makes it plentiful and inexpensive to use as a rocket fuel. They also reported that the initial test of the rocket engine produced more than just thrust; it also created shock diamonds, which are commonly produced with other types of high-temperature rocket firings. The team is scheduled to conduct another test soon, this time as a demonstration for an unknown client. They also confirmed that the initial test went as planned and that they were pleased with the test firing, calling it a "significant" moment in rocket history.
Notably, other companies have tried using plastic waste as a rocket fuel, Virgin Galactic being the most well-known. In 2014, the idea was tested by the company and abandoned after a test did not go as hoped. Pulsar Fusion has made announcements periodically regarding its plans for such an engine; they expect rockets using it to carry satellites and eventually people into space.
Rocket test launch for Space Force fails to reach orbit
pulsarfusion.com/
© 2021 Science X Network
Engineers conduct test of rocket engine powered by plastic waste (2021, November 29)
retrieved 30 November 2021
from https://techxplore.com/news/2021-11-rocket-powered-plastic.html
This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no
part may be reproduced without the written permission. The content is provided for information purposes only.
Tags: conductEngineengineersPlasticpoweredRockettestwaste
Why does my blood pressure rise when I go to the GP? DR MARTIN SCURR answers your health questions
Rapper ChillinIT is hurled to the ground and kneed in the head by police in Sydney
Credit: Shutterstock Researchers at ETH...
Support for populist politics 'collapsed' during the pandemic – global report
Support for populist parties and...
A Ranking of the Top Superhero Films to Hit Screens
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The Best Plans Currently On Offer In Australia


The European Fund is used for the development of Urantia Book reader communities throughout Europe and supports projects, activities and regional/local events in the various European regions. Funds may be used to stimulate study activities and coordinate localized events, arranging continental conferences, providing gift books to study groups, supporting book placement programs in libraries and universities, and utilizing the expanding global communication technology to make it possible for people to come together and engage in study and communion.
If people don't connect with others, books can end up sitting on dusty shelves. There are now more than one million copies of The Urantia Book in the world, and this is an amazing achievement of generations of collective energies and efforts. Now is the time to make an equal commitment to building the Urantia community.
Urantia Association has friends on the ground and hearts in service across the globe, uniting students of the revelation. Our projects are funded by donations made by average people on average incomes; they are not funded by other organizations or some benevolent megadonor. We build conferences and finance projects in Europe $20 at a time.
Now is the time to support our Urantia community with the same zeal as creating new translations and new editions of The Urantia Book.


The effect of specialized dairy breeds on udder cistern size in Tsigai crossbreds – Výzkumný ústav živočišné výroby, v.v.i.
MARGETÍN, Milan, MAKOVICKÝ, P., MILERSKI, Michal, APOLEN, Dušan, DEBRECÉNI, O. a ORAVCOVÁ, M. The effect of specialized dairy breeds on udder cistern size in Tsigai crossbreds. Slovak Journal of Animal Science, 2011, roč. 44(4), s. 146-153. ISSN .
Many scientific papers describing the cistern size of ewe's mammary gland and its impact on ewe adaptation to machine milking have been published until now. Various daily sheep breeds have been investigated by a number of authors (Bruckmaier and Blum, 1992; Bruckmaier et al, 1997; Caja et al, 1999; Margetin et al, 2002, 2003, 2010; Franz et al, 2003; Milerski et al, 2005, Castillo et al, 2008; Macuhova et al, 2010). The udder cistern measurements taken by ultrasonography techniques have also been studied in dairy goats by Wojtowski et al. (2006) and in dairy cows by Ayadi et al (2003). It was shown that udder scanning by ultrasonography is a suitable tool to study ewe's mammary gland throughout the whole lactation. This is a simple procedure with no special requirements. Nudda et al. (2000), Makovicky (2009) and Margetin et al. (2010) made a recommendation for using sonographic measurements as a good indicator of the cistern size in ewes. Sonographic measurements may be effective criteria for selection of ewes as they enable to identify individuals with high milk yield.


text:
Borderlines Vol. I
Borderlines Vol. II
Borderlines Vol. III
Homes and Histories
Women Under Siege
SELECT PROJECTS
Borderlines Living Room Art
Third Worlds: Third Ward / Karachi
Award-Winning Art Car
Honoring Dissent/Descent
UH Archives
Support VBB
Voices Breaking Boundaries
Through literary and visual arts, Voices Breaking Boundaries provokes awareness and dialogue about social justice issues across and within local and global borders.
What Is Home? (2015); photo by Paul Hester
Sehba Sarwar founded Voices Breaking Boundaries in 2000, inspired by a poem she wrote in 1999 about political events unfolding in Pakistan.
Looking for a space to perform her work, she invited four women writers/artists – Christine Choi, Marcela Descalzi, Donna Perkins, and Jacsun Shah – to join her in starting a literary collective. Sarwar received project grants from the Houston Arts Alliance (then called Cultural Arts Council of Houston/Harris County), and the collective hosted bi-monthly readings at a Houston bookstore. The response ignited Sehba's determination to produce a series of multi-sensory experiences enriched by open mic, music and dance.
The VBB ball was rolling. Milestone highlights:
The University of Houston installs permanent VBB archives that chronicle the organization's ongoing history.
VBB is featured in Houston History, a quarterly magazine published by the Center for Public History at the University of Houston. The feature story is accompanied by a month-long exhibition of VBB's archived materials at The Heritage Society Museum Gallery in downtown Houston.
Working with editors Margot Backus and Maria Gonzalez and layout artist Joshua Turner, VBB publishes BORDERLINES Volume One and Volume Two, that contain art from Living Room Art shows as well as essays, poems and interviews from border regions.
UH History professor Kairn Klieman teaches a public history graduate level course that focuses on the development of VBB and Sarwar's history as an activist and artist.
Sarwar develops BORDERLINES, a project that is expanded beyond Houston and Karachi to explore border issues between North America and select South Asian countries (Bangladesh, India, Pakistan).
Sarwar is awarded Artist-in-Residence at the Mitchell Center for the Arts (University of Houston), where she develops her What is Home? project.
VBB is awarded its first National Endowment for the Arts (NEA) grant through which Sarwar collaborates with Houston-based and Karachi based-artists to create two productions, Women Under Siege and Homes and Histories, that explore how religious extremism impacts women and how the slavery of black communities affected both Houston and Karachi.
Sarwar donates her 1992 Honda Civic hatchback to VBB and collaborates with artist Eric Hester to create an Art Car, Revolution, that contains nine television screens, a microphone, images of inspiring artists including Faiz Ahmed Faiz and Patti Smith, and that is decorated with Pakistani truck art motifs from Karachi. In 2011, the car wins a Freedom of Speech award at Houston's legendary Orange Show Art Car Parade.
VBB hosts a reading and performance donated by punk rock icon Patti Smith following a chance meeting with Sehba Sarwar in New York after a protest against the war in Iraq.
Sehba Sarwar starts a new stream of Living Room Art productions at her own home in East Houston; the show is dedicated to her father Dr. Mohammad Sarwar, a doctor and activist in Pakistan, and Daniel Bustamente, an activist in Houston.
VBB initiates a pop-up multidisciplinary series in Houston's East End through which artists exploring race, women's rights, education, and GLBT issues are given voice.
VBB is awarded its first Andy Warhol Foundation for the Visual Arts award to deepen its creation of alternative pop-up art around Houston.
VBB's first Living Room Art (LRA) Production initiated by Oskar Sonnen takes place at Jaspal Subhlok's home in Houston's Montrose neighborhood, drawing more than 200 people.
The organization produces its Words for Peace multidisciplinary series in response to the biases emerging in the community after 9/11; productions are held at DiverseWorks where VBB has started officing at the invitation of DiverseWorks Interim Performance Arts Director Oskar Sonnen.
Through grants and funding received by Sarwar, VBB initiates writing, performance and video workshops at Furr, Sharpstown and Lee High Schools. Some workshops culminate with public performance at DiverseWorks, where Sarwar serves as Literary Curator.
Based on the success of the South Asian Film Festivals, and with the support of several community members including Krupa Parikh, VBB incorporates as a non-profit 501(c)3 arts organization.
VBB initiates South Asian Film Festivals, a collaboration between Himal South Asia and VBB. With the support of Marian Luntz, Film Director at the Museum of Fine Arts Houston (MFAH) Film Department, screenings are held at the MFAH and in collaboration with Fotofest.
Support Voices Breaking Boundaries by Donating Today!
Stay in touch with Sehba Sarwar and VBB!
Join our mailing list by filling out the form.
For more information, please call +1 713 524 7821 or email info@vbbarts.org.
©2016 VOICES BREAKING BOUNDARIES. ALL RIGHTS RESERVED. DESIGNED BY BLACK + GRAY STUDIO.


text:
Q: cordova-android-play-services-gradle-release: ERROR: EXCEPTION: TypeError: arg.slice is not a function When I upgrade the cordova plugin "cordova-android-play-services-gradle-release" from version 3.0.0 to 4.0.0 I am getting the following error :
Cordova command 'build' started ...
cordova-android-play-services-gradle-release: ERROR: EXCEPTION: TypeError: arg.slice is not a function
cordova-android-support-gradle-release: Android platform: V7+
cordova-android-support-gradle-release: No custom version found in package.json - using plugin default
cordova-android-play-services-gradle-release: ERROR: EXCEPTION: TypeError: arg.slice is not a function
cordova-android-support-gradle-release: Android platform: V7+
cordova-android-support-gradle-release: No custom version found in package.json - using plugin default

followed by other error :
BUILD FAILED in 10s
35 actionable tasks: 35 executed
{ Error: /Users/.../android/platforms/android/gradlew: Command failed with exit code 1 Error output:
Note: /Users/..../android/platforms/android/CordovaLib/src/org/apache/cordova/engine/SystemCookieManager.java uses or overrides a deprecated API.
Note: Recompile with -Xlint:deprecation for details.
Note: Some input files use or override a deprecated API.
Note: Recompile with -Xlint:deprecation for details.
Note: Some input files use unchecked or unsafe operations.
Note: Recompile with -Xlint:unchecked for details.
D8: Program type already present: android.support.v4.app.INotificationSideChannel$Stub$Proxy

FAILURE: Build failed with an exception.

* What went wrong:
Execution failed for task ':app:transformClassesWithMultidexlistForDebug'.
> com.android.build.api.transform.TransformException: Error while generating the main dex list:
  Error while merging dex archives:
  Learn how to resolve the issue at https://developer.android.com/studio/build/dependencies#duplicate_classes.
  Program type already present: android.support.v4.app.INotificationSideChannel$Stub$Proxy

* Try:
Run with --stacktrace option to get the stack trace. Run with --info or --debug option to get more log output. Run with --scan to get full insights.

* Get more help at https://help.gradle.org

BUILD FAILED in 10s
    at ChildProcess.whenDone (/Users/.../android/node_modules/cordova-common/src/superspawn.js:135:23)
    at ChildProcess.emit (events.js:198:13)
    at ChildProcess.EventEmitter.emit (domain.js:466:23)
    at maybeClose (internal/child_process.js:982:16)
    at Process.ChildProcess._handle.onexit (internal/child_process.js:259:5)
  stderr:
   'Note: /..../CordovaLib/src/org/apache/cordova/engine/SystemCookieManager.java uses or overrides a deprecated API.\nNote: Recompile with -Xlint:deprecation for details.\nNote: Some input files use or override a deprecated API.\nNote: Recompile with -Xlint:deprecation for details.\nNote: Some input files use unchecked or unsafe operations.\nNote: Recompile with -Xlint:unchecked for details.\nD8: Program type already present: android.support.v4.app.INotificationSideChannel$Stub$Proxy\n\nFAILURE: Build failed with an exception.\n\n* What went wrong:\nExecution failed for task \':app:transformClassesWithMultidexlistForDebug\'.\n> com.android.build.api.transform.TransformException: Error while generating the main dex list:\n  Error while merging dex archives: \n  Learn how to resolve the issue at https://developer.android.com/studio/build/dependencies#duplicate_classes.\n  Program type already present: android.support.v4.app.INotificationSideChannel$Stub$Proxy\n\n* Try:\nRun with --stacktrace option to get the stack trace. Run with --info or --debug option to get more log output. Run with --scan to get full insights.\n\n* Get more help at https://help.gradle.org\n\nBUILD FAILED in 10s\n',
  stdout:
   '\n> Configure project :app\n+-----------------------------------------------------------------\n| cordova-android-support-gradle-release: 27.+\n+-----------------------------------------------------------------\nCould not find google-services.json while looking in [src/nullnull/debug, src/debug/nullnull, src/nullnull, src/debug, src/nullnullDebug]\nregisterResGeneratingTask is deprecated, use registerGeneratedResFolders(FileCollection)\nCould not find google-services.json while looking in [src/nullnull/release, src/release/nullnull, src/nullnull, src/release, src/nullnullRelease]\nregisterResGeneratingTask is deprecated, use registerGeneratedResFolders(FileCollection)\n\n> Task :app:preBuild UP-TO-DATE\n> Task :CordovaLib:preBuild UP-TO-DATE\n> Task :CordovaLib:preDebugBuild UP-TO-DATE\n> Task :CordovaLib:checkDebugManifest\n> Task :CordovaLib:processDebugManifest\n> Task :app:preDebugBuild\n> Task :CordovaLib:compileDebugAidl NO-SOURCE\n> Task :app:compileDebugAidl NO-SOURCE\n> Task :CordovaLib:packageDebugRenderscript NO-SOURCE\n> Task :app:compileDebugRenderscript\n> Task :app:checkDebugManifest\n> Task :app:generateDebugBuildConfig\n> Task :app:prepareLintJar\n> Task :app:generateDebugSources\n> Task :CordovaLib:compileDebugRenderscript\n> Task :CordovaLib:generateDebugBuildConfig\n> Task :CordovaLib:generateDebugResValues\n> Task :CordovaLib:generateDebugResources\n> Task :CordovaLib:packageDebugResources\n> Task :CordovaLib:generateDebugRFile\n> Task :CordovaLib:prepareLintJar\n> Task :CordovaLib:generateDebugSources\n> Task :CordovaLib:javaPreCompileDebug\n\n> Task :CordovaLib:compileDebugJavaWithJavac\n\n> Task :CordovaLib:processDebugJavaRes NO-SOURCE\n> Task :CordovaLib:transformClassesAndResourcesWithPrepareIntermediateJarsForDebug\n> Task :app:javaPreCompileDebug\n> Task :app:mainApkListPersistenceDebug\n> Task :app:generateDebugResValues\n> Task :app:generateDebugResources\n\n> Task :app:processDebugGoogleServices\nParsing json file: /Users/../android/platforms/android/app/google-services.json\n\n> Task :app:mergeDebugResources\n> Task :app:createDebugCompatibleScreenManifests\n> Task :app:processDebugManifest\n> Task :app:processDebugResources\n\n> Task :app:compileDebugJavaWithJavac\n\n> Task :app:compileDebugNdk NO-SOURCE\n> Task :app:compileDebugSources\n> Task :app:mergeDebugShaders\n> Task :app:compileDebugShaders\n> Task :app:generateDebugAssets\n> Task :CordovaLib:mergeDebugShaders\n> Task :CordovaLib:compileDebugShaders\n> Task :CordovaLib:generateDebugAssets\n> Task :CordovaLib:packageDebugAssets\n> Task :app:mergeDebugAssets\n> Task :app:validateSigningDebug\n> Task :app:signingConfigWriterDebug\n> Task :app:transformClassesWithDexBuilderForDebug\n\n> Task :app:transformClassesWithMultidexlistForDebug FAILED\n35 actionable tasks: 35 executed\n',
  code: 1 }

My application contains many other cordova plugins and I can not figure out what cause this error. Can anyone help me?
Any idea is welcome.

redpajama_set_name: RedPajamaStackExchange


Laura Thompson is a local artist and art teacher. She graduated from JMU with a BFA in Graphic Design and her art education license in 2003, and has taught art in elementary and middle schools in the Shenandoah Valley since 2004. In 2014, she graduated with her master's in art education from JMU, officially becoming a "Double Duke." She has taught art classes to both children and adults, and loves sharing her skills and knowledge with others. Most recently, she has been painting with oils, though she also enjoys creating mixed-media artworks, primarily with graphite and watercolor. She is actively participating in shows, and feels it is critical for her personal growth that she continues creating art. She believes it is important for every person to incorporate art into their life in some way, whether through crafting, experimenting, DIYing, or just appreciating it.


text:
Downward price trend continues, PS plunges again
David Platt, Plastics News Europe
The downward price trend for standard thermoplastics, which started during the second half of April, continued into May. Polyolefin feedstock costs were unchanged in May while styrene monomer plunged even further. Supply is now more than adequate to meet fairly lackluster demand.
In May, PE prices fell between €10-30/tonne and PP was down €10-15/tonne, despite a rollover for both the ethylene and propylene contract prices. PET prices were also lower again following further reduction in key raw material costs. Only PVC compound prices firmed, largely as a result of the severe shortages of titanium dioxide.
PS prices plummeted once more after the styrene monomer reference price fell by €245/tonne. Again, producers did not pass through the full cost reduction to processors.
Supply lengthens
Material availability has improved during the second quarter as most European refinery maintenance so far this year took place in the first quarter, with the second quarter seeing a return to full production. Producers are well stocked and there is more than sufficient material available across all polymer classes. The stronger euro exchange rate is also encouraging a larger volume of imported material from Asia and the Middle East into Europe.
A summary of the latest supply-related developments is presented below:
• Dow Chemical announced 12 May investments totaling $4 billion into the expansion of PE, in particular, over five years. While most of these investments are set to be made in the USA, Dow also announced the construction of a new 450,000 tonnes/year HDPE line in Europe producing high-quality grades for pressure pipes and fittings as well as caps and closures.
• Since 6 May Total's refinery facilities are successively being shut down in Feyzin, near Lyon, France due to a large strike, with employees demanding better working conditions. An end to the walkout was expected by 19 May.
• Reconstruction of Total's facility in Carling, France, which started in 2013, has been officially completed and inaugurated.
• Only one of Huntsman's two MDI production plants in the Netherlands resumed operation early May following maintenance programs. Huntsman has encountered "an unforeseen technical issue" that has prevented the second MDI unit from restarting. No precise date for a restart could be given.
• German plastic producer Covestro confirmed 28 April that force majeure is declared on the PU precursor MDI (polymer). The reason for this is an unforeseen failure at its plant in Brunsbüttel, Germany. It is unclear when production of the isocyanate can be resumed.
• PVC manufacturer Vynova Group declared force majeure 21 April on sodium hydroxide from Runcorn, UK. The reason is an "unforeseen disruption" in the plant for ethylene dichloride (EDC) at the site. As a result, PVC production in Wilhelmshaven, Germany, which is supplied by Runcorn with EDC precursor, could be affected.
Demand subdued
In early May, polymer demand was lower than would normally be expected. Plastic processors were for the most part well stocked and in no hurry to buy. Many were waiting to see whether prices fell further before replenishing inventories.
June outlook
Crude oil prices edged higher in May due to an expectation that the OPEC meeting in Vienna 25 May will agree to further control of output. On the other hand, as the return of cracker capacity arrives, there could be downward pressure on June contract prices. Furthermore, the first half of June includes the public holiday for Whitsun, which may mean that demand gets off to a slow start.
For the full report click here.


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