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Production simulation by means of a structure tensor‐based framework of anisotropic plasticity
Author(s) -
Vladimirov Ivaylo N.,
Reese Stefanie
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210390
Subject(s) - hyperelastic material , anisotropy , helmholtz free energy , plasticity , isotropy , finite strain theory , dissipation , tensor (intrinsic definition) , hardening (computing) , materials science , work (physics) , mechanics , nonlinear system , classical mechanics , statistical physics , physics , mathematics , geometry , thermodynamics , finite element method , layer (electronics) , quantum mechanics , composite material
In this work, we discuss a hyperelasticity‐based concept of finite strain plasticity with combined hardening using evolving structure tensors to represent the evolution of elastic and plastic anisotropy. By defining the Helmholtz free energy density and the yield surface as functions of the evolving structure tensors, we are able to describe both evolving elastic and plastic anisotropy, respectively. The model considers also nonlinear kinematic and isotropic hardening and is derived from a thermodynamic framework based on the multiplicative split of the deformation gradient. Exploiting the dissipation inequality leads to the important result that the model includes only symmetric tensor‐valued internal variables. Evolution of anisotropy is investigated by means of simulations of cylindrical deep drawing of metal sheets. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)