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Finite Strain Constitutive Model of Evolving Elastic and Plastic Anisotropy by Means of Structure Tensors

[+] Author Affiliations
Ivaylo N. Vladimirov, Stefanie Reese

RWTH Aachen University, Aachen, Germany

Paper No. ESDA2012-82766, pp. 509-517; 9 pages
  • ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis
  • Volume 1: Advanced Computational Mechanics; Advanced Simulation-Based Engineering Sciences; Virtual and Augmented Reality; Applied Solid Mechanics and Material Processing; Dynamical Systems and Control
  • Nantes, France, July 2–4, 2012
  • Conference Sponsors: International
  • ISBN: 978-0-7918-4484-7
  • Copyright © 2012 by ASME


In this paper, a finite strain constitutive model for evolving elastic and plastic anisotropy combining nonlinear isotropic and kinematic hardening is presented. The evolution of elastic anisotropy is described by defining the Helmholtz free energy as an isotropic function of a family of evolving structure tensors. In addition, plastic anisotropy is modelled via the dependence of the yield surface on the same family of structure tensors. Exploiting the Clausius-Duhem inequality leads to the interesting result that all tensor-valued internal variables are symmetric. Thus, the integration of the evolution equations can be efficiently performed by means of an implicit algorithm that automatically retains the symmetry of the internal variables in every time step. The material model is used as a user material subroutine UMAT infinite element package ABAQUS/Standard, by means of which the occurrence of earing during cylindrical deep drawing is simulated.

Copyright © 2012 by ASME



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