Papers by Keyword: Elasto-Plasticity

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Authors: Zohra Sendi, Carl Labergère, Khemais Saanouni, Hedi Belhadj Salah
Abstract: The Finite Element Method (FEM) is today the most widely used in numerical simulation of forming processes, due essentially to the continuous improvement of the FEM over the years and the simplicity of its implementation. However, this method has some limitations such as the distortion of elements under large inelastic deformation and the influence of the mesh on the results in several applications. The simulation of metal forming process with large plastic strain is a classical example where the successive remeshing is often the proposed solution in this case. But the remeshing raises the problems of precision and computing time. In this context and in order to avoid the remeshing process, a Meshless method is experimented in the solving of an elastoplastic problem coupled to the isotropic ductile damage. An Element Free Galerkin (EFG) method based on Moving Least Square (MLS) concept is considered in this proposal. A two-dimensional Mechanical problem was studied and solved by a Dynamic-Explicit resolution scheme where the material behaviour is based on an isotropic hardening fully coupled to ductile damage model. In a first step a parametric study is conducted in order to find the most influent parameters on the accuracy of the results. The effect of the number of nodes, of support nodes, of quadrature points, the effect of the time-step and the support domain size are analysed and optimal values are found. In a second step, the meshless results are compared with those of the finite element method and some concluding remarks relative to the accuracy and the computing time are given.
Authors: Mathias Wallin, Matti Ristinmaa, Mattias Olsson
Abstract: A constitutive model for ductile porous material is formulated within the thermodynamic framework. A yield function based on the lower-bound solution for a cylindrical void model embedded in a plastic matrix is proposed. The new yield function is compared to the classical Gurson yield function using cell model calculations. The results reveal that the proposed yield function agreed well with the plastic region found from the cell model calculations. In addition to the influence of the void-volume ratio, the elastic part of the free energy is dependent on a scalar damage field which allows the elasticity to be influenced by the void-volume fraction. The degradation is controlled by a scalar valued damage field and enters the formulation via the Helmholtz's free energy. This dependence allows the elastic properties to naturally depend upon the damage accumulation. The numerical treatment of the model is derived and the capability of the model is demonstrated via numerical simulation of the necking of an axi-symmetric bar.
Authors: Fabio de Angelis
Abstract: A general formulation of constitutive relations in non-smooth elastoplasticity is presented. The treatment applies to general non-smooth plasticity problems and to problems characterized by non-smooth yield criteria or dealing with non-differentiable functions. The mathematical tools and instruments of convex analysis and subdifferential calculus are suitably applied since they provide the proper mathematical instruments for dealing with non-smooth problems and non-differentiable functions. General formulations of constitutive relations and evolutive laws in non-smooth elastoplasticity are illustrated within the presented theoretical framework. Connections between the proposed mathematical treatment and the classical relations in elastoplasticity are illustrated and discussed in detail. The presented generalized treatment is equipped with considerable advantages since it shows to be ideally suited for the development of variational formulations of structural problems in non-smooth elastoplasticity.
Authors: Lapo Gori, Roque Luiz da Silva Pitangueira, Samuel Silva Penna, Jamile Salim Fuina
Abstract: This paper summarizes the implementation of an elasto-plastic constitutive model for a micro-polar continuum in the constitutive models framework of the software INSANE (INteractive Structural ANalysis Environment). Such an implementation is based on the tensorial format of a unified constitutive models formulation, that allows to implement different constitutive models independently on the peculiar numerical method adopted for the solution of the problem. The basic characteristics of the micro-polar continuum model and of the unified formulation of constitutive models are briefly recalled. A generalization of the micro-polar model is then introduced in order to include this model in the existent tensor-based formulation. Finally, an enhanced version of the general closest-point algorithm, ables to manage the generalized micro-polar formulation, is derived. A strain localization problem modeling illustrates the implementation.
Authors: Otto T. Bruhns
Abstract: Recently it has been demonstrated that the classical Prandtl/Reuss theory based on the additive split of the deformation rate contrary to what is believed so far is possible to establish a consistent Eulerian rate formulation for finite elastoplasticity. Here, we attempt to place this Eulerian formulation on the thermodynamic grounds by extending it to a general case with thermal effects.
Authors: Vladimir I. Andreev
Abstract: It is generally considered within analysis the residual stresses that unloading occurs on elastic law. For large initial loads, some plasticity theories believe that during unloading secondary plastic deformation can occur. The distinctive work provides a new theorem of unloading, which takes into account irreversible changes in the mechanical characteristics of the material under load. There is an example of the analysis of residual stresses corresponding to the given theorem.
Authors: Abel Cherouat, Laurence Giraud-Moreau, Houman Borouchaki
Abstract: This paper presents an advanced numerical methodology which aims to improve virtually any metal forming processes. It is based on elastoplastic constitutive equations accounting for non-linear mixed isotropic and kinematic hardening “strongly” coupled with isotropic ductile damage. During simulation of metal forming processes, where large plastic deformations with ductile damage occur, severe mesh distorsion takes place after a finite number of incremental steps. Hence an automatic mesh generation with remeshing capabilities is essential to carry out the finite element analysis. Besides, when damage is taken into account a kill element procedure is needed to eliminate the fully damaged elements in order to simulate the growth of macroscopic cracks. The necessary steps to remesh a damaged structure in finite element simulation of forming processes including damage occurrence (initiation and growth) are given. An important part of this procedure is constituted by geometrical and physical error estimates. The meshing and remeshing procedures are automatic and are implemented in a computational finite element analysis package (ABAQUS/Explicit solver using the Vumat user subroutine). Some numerical results are presented to show the capability of the proposed procedure to predict the damage initiation and growth during the metal forming processes.
Authors: Jian Fu Shao, F. Bourgeois, O. Ozanam
Authors: Jun Liu, Gao Lin
Abstract: An elastoplastic-anisotropic damage constitutive model for the description of nonlinear behavior of concrete is presented. The yield surface is developed in effective stress spaces, which takes into account the hardening effect and better match the experimental data. The stiffness degradation and softening effect are considered in the framework of continuum damage mechanics formulation. The second-order damage tensor is used to characterize the anisotropy induced by the orientation of microcracks. In order to simulate the unilateral effect, the elastic Helmholtz free energy is decomposed into a volumetric part and a deviatoric part. The different behavior under tensile and compressive loadings is modeled by using different variables in effective stress and damage tensor. Numerical results of the model accord well with experimental results at the material and structural levels.
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