<http://purl.org/dc/terms/description>
"The applicability and accuracy of existing finite element formulation methods for finite\r\nstrain deformation and metal forming problems are investigated. It is shown that the existing\r\nformulation methods, both Lagrangian and Eulerian type, are not suitable nor efficient for\r\nlarge deformation problems especially when boundary conditions change during deformation,\r\nas is the case in most metal forming problems. This creates a need for a more general and\r\nefficient type of formulation. An Arbitrary Lagrangian-Eulerian (ALE) method is presented\r\nfor the general application in solid mechanics and large deformation problems. A consistent\r\nALE formulation is developed from the virtual work equation transformed to an arbitrary\r\ncomputational reference configuration. The formulation presents a general approach to ALE\r\nmethod in solid mechanics applications. It includes load correction terms and it is suitable\r\nfor both rate-dependent as well as rate-independent material constitutive laws. The proposed\r\nformulation reduces to both updated Lagrangian and Eulerian formulations as special cases.\r\nThe formulation is presented in a form that makes the programming an extension to existing\r\nLagrangian and Eulerian type programs.\r\nAn efficient mesh motion scheme for ALE formulation is developed with a procedure for\r\nhandling boundary motion within the scheme, which can ensure homogeneous mesh results. A\r\npractical and more efficient numerical method is presented to handle supplementary constraint\r\nequations on element level rather than on the global level. Different numerical algorithms for\r\nthe integration of the rate type constitutive equation are investigated and coupled with the return\r\nmapping algorithm to provide plastic incremental consistency. A numerical procedure for stress\r\nintegration is developed based on the physical meaning of stress. Jaumann and Truesdell rates\r\nare taken as the objective stress rates in the constitutive equation. An alternative numerical treatment for rate of deformation tensor [sup t]D[sub ij] is presented to maintain incremental objectivity\r\nof the tensor. It is shown by numerical examples that the use of Truesdell stress rate with a\r\ndeveloped numerical integration procedure gives consistently more accurate results than other\r\nprocedures presented. An algorithm for updating material associated properties is presented\r\nand applied in simulation of various metal forming problems.\r\nA 2D finite element program, ALEFE, based on the presented formulation is developed and\r\ntested. The program may reduce to an updated Lagrangian or Eulerian methods as special cases.\r\nThe mesh motion for the whole domain is controlled by the motion of the boundary nodes.\r\nThe program can handle unsymmetric stiffness matrices and coupled displacements/velocity\r\nboundary conditions. The input data is designed to be similar to available commercial finite\r\nelement codes, so that the data generation phase may be directly imported from these programs.\r\nThe output data format is designed to be compatible with general graphic simulation and data\r\nprocessing commercial softwares, so that contour, x-y and deformed mesh plots may be easily\r\ncreated from the output data of ALEFE.\r\nVarious benchmark and practical problems are simulated by the developed program. Practical\r\nsimulation cases include flat punch forging process, sheet metal extrusion process, necking\r\nbifurcation of a bar in tension, a steady strip rolling and compression between wedge-shaped\r\ndies. Numerical results are compared with analytical solutions or experimental results available\r\nin literature."@en
<https://open.library.ubc.ca/cIRcle/collections/ubctheses/831/items/1.0080928>