Total-FETI domain decomposition method for solution of elasto-plastic problems

In this paper we present an algorithm for the parallel solution of the rate-independent elasto-plastic problems with kinematic hardening. We assume the von Mises plastic criterion and the associated plastic flow rule. The time discretization is based on the implicit Euler method. The corresponding one-time-step problem is formulated in the incremental form with respect to the unknown displacement and discretized spatially by the finite element method. We use an ‘external’ algorithm based on a linearization of the elasto-plastic stress–strain relation by the corresponding tangential operator and we parallelize the arising linearized problem by the Total-FETI method. The numerical experiments were carried out using our novel C/C++ library FLLOP (FETI Light Layer On top of PETSc) at HECToR supercomputer located at EPCC, UK.     

Finite element modelling of wooden structures at large deformations and brittle failure prediction

This paper presents a constitutive wood model that accounts for both hardening associated with material densification at large compressive deformations and brittle failure modes. The model is adapted from previous work by the authors and has been modified to deal with wood behaviours. The main novelty of the model is the coupling between the anisotropic plasticity and the ductile densification. The model developed is successfully implemented in the commercial ABAQUS software. Validation was made for uniaxial compressive loadings and an application on a three-points bending test. The results obtained, for the uniaxial compressive loadings, demonstrate the capability of the model to simulate the wood behaviour at large compressive deformations and show clearly the effect of the densification on the plastic behaviour. The result obtained for the three-points bending test shows a good implementation of the brittle failure criterion and demonstrates the suitability of the developed model to analyse and design wooden structures.     

NICE—An explicit numerical scheme for efficient integration of nonlinear constitutive equations

The paper presents a simple but efficient new numerical scheme for the integration of nonlinear constitutive equations. Although it can be used for the integration of a system of algebraic and differential equations in general, the scheme is primarily developed for use with the direct solution methods for solving boundary value problems, e.g. explicit dynamic analysis in ABAQUS/Explicit. In the developed explicit scheme, where no iteration is required, the implementation simplicity of the forward-Euler scheme and the accuracy of the backward-Euler scheme are successfully combined. The properties of the proposed NICE scheme, which was also implemented into ABAQUS/Explicit via User Material Subroutine (VUMAT) interface platform, are compared with the properties of the classical forward-Euler scheme and backward-Euler scheme. For this purpose two highly nonlinear examples, with the von Mises and GTN material model considered, have been studied. The accuracy of the new scheme is demonstrated to be at least of the same level as experienced by the backward-Euler scheme, if we compare them on the condition of the same CPU time consumption. Besides, the simplicity of the NICE scheme, which is due to implementation similarity with the classical forward-Euler scheme, is its great Advantage.     

Finite element analysis of non-isothermal multiphase geomaterials with application to strain localization simulation

Finite element analysis of non-isothermal elasto-plastic multiphase geomaterials is presented. The multiphase material is modelled as a deforming porous continuum where heat, water and gas flow are taken into account. The independent variables are the solid displacements, the capillary and the gas pressure and the temperature. The modified effective stress state is limited by the Drucker-Prager yield surface for simplicity. Small strains and quasi-static loading conditions are assumed. Numerical results of strain localization in globally undrained samples of dense, medium dense and loose sands and isochoric geomaterial are presented. A biaxial compression test is simulated assuming plane strain condition during the computations. Vapour pressure below the saturation water pressure (cavitation) develops at localization in case of dense sands, as experimentally observed. A case of strain localization induced by a thermal load where evaporation takes place is also analysed. Dedicated to Professor S. Valliappan in occasion of his retirement     

Three dimension profile extrusion simulation using meshfree method

A meshfree method based on reproducing kernel approximation and point collocation is presented for analysis of 3D profile extrusion processes. The point collocation method is a true meshfree method without the employment of a background mesh. We show that, in a point collocation approach, the implementation of program does not need the background mesh, which is a very time consuming process in a Galerkin method for integration. Among the points of the meshfree model, there is no connecting information. A mesh quality control method with mold interpenetration checking based on the Delaunay Bowyer-Watson algorithm is introduced to produce the topological relations, which enable us to show meshfree simulation results using the same procedure as in the finite element method. A C-shape profile extrusion application example is presented and compared with the finite element method to verify the proposed method.     

A Comparison of Mapping Algorithms for Hierarchical Adaptive FEM in Finite Elasto-Plasticity

The aim of this contribution is a comparison of different mapping techniques usually applied in the field of hierarchical adaptive FE-codes. The calculation of mechanical field variables for the modified mesh is an important but sensitive aspect of adaptation approaches of the spatial discretization. Regarding non-linear boundary value problems procedures of mesh refinement and coarsening imply the determination of strains, stresses and internal variables at the nodes and the Gauss points of new elements based on the transfer of the required data from the former mesh. The kind of mapping of the field variables affects the convergence behaviour as well as the costs of an adaptive FEM-calculation in a non-negligible manner. In order to improve the stability as well as the efficiency of the adaptive process a comparison of different mapping algorithms is presented and evaluated. Within this context, the mapping methods taken into account are

含一级相变热弹塑性材料的热传导方程及应用

由金属物理学的基本概念出发融合非线性连续介质力学中内变量方法,给出含一级相变热弹塑性材料的热传导方程及在金属凝固、淬火温度场分析中的应用实例。     

APPLICATION OF INTEGRATION ALGORITHEMS FOR ELASTO-PLASTICITY CONSTITUTIVE MODEL FOR ANISOTROPIC SHEET MATERIALS

Two algorithms of computing stress increment by using the elasto-plasticity constitutive model are firstly formulated, which are the Euler integration method and the radial return method. Hill'48 anisotropic yield criterion is used. The Euler integration method can not obtain more accurate computation of the stress increment as the radial return method unless enough subintervals are taken, by which the Euler integration method will take excessive computing time. Without decreasing any accuracy, the radial return method can save much time. Finally, a square cup deep drawing from NUMISHEET'93 benchmarks is simulated with a self-developed code SheetForm in order to investigate the accuracy and efficiency of the radial return method.     

Application of generalized measures to an orthotropic finite elasto-plasticity model

A numerical study of finite orthotropic elasto-plasticity based on generalized stress–strain measures is presented. The anisotropic constitutive equations are represented by isotropic tensor functions. A simple additive decomposition of strains can be performed due to the formulation in generalized measures. Furthermore, the plasticity model does not depend on special properties of any particular measure. The required projection tensor is constructed exploiting the coaxiality of the generalized deformation tensor with the right Cauchy–Green tensor. An efficient algorithmic implementation is proposed. Finally, we discuss representative numerical examples for orthotropic elasto-plasticity, where finite deformations occur.     

The complex variable element-free Galerkin (CVEFG) method for elasto-plasticity problems

Based on the complex variable moving least-squares (CVMLS) approximation and element-free Galerkin (EFG) method, the complex variable element-free Galerkin (CVEFG) method for two-dimensional elasto-plasticity problems is presented in this paper. The CVMLS approximation is an approximation method for a vector function. Under the same node distribution the meshless method based on the CVMLS approximation has higher precision than the one based on the moving least-squares (MLS) approximation. For two-dimensional elasto-plasticity problems, the Galerkin weak form is employed to obtain the equations system, and the penalty method is used to apply the essential boundary conditions, then the corresponding formulae of the CVEFG method for two-dimensional elasto-plasticity problems are obtained. Compared with the EFG method, the CVEFG method can obtain greater precision. For the purposes of demonstration, some selected numerical examples are solved using the CVEFG method.