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Simulation of Rate Dependent Plasticity of Polymers
Author(s) -
Shaban Ahmed,
Mahnken Rolf
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610185
Subject(s) - finite element method , stress space , constitutive equation , plasticity , stress (linguistics) , mathematics , weighting , strain rate , materials science , plane stress , mathematical analysis , nonlinear system , mechanics , physics , composite material , thermodynamics , linguistics , philosophy , quantum mechanics , acoustics
Polycarbonate is an amorphous polymer which exhibits nonlinear deformation before failure. It shows a pronounced strength‐differential effect between compression and tension. Strain rate influences the mechanical response of the polycarbonate. In particular, the yield stress is increased with increasing strain rate. The concept of stress mode dependent weighting function is used in the proposed model to simulate the asymmetric effects for different loading speeds. In this concept, an additive decomposition of the flow rule is assumed into a sum of weighted stress mode related quantities. The characterization of the stress modes is obtained in the octahedral plane of the deviatoric stress space in terms of the mode angle, such that stress mode dependent scalar weighting functions can be constructed. The resulting evolution equations are updated using a backward Euler scheme and the algorithmic tangent operator is derived for the finite element equilibrium iteration. The numerical implementation of the resulting set of constitutive equations is used in a finite element program for parameter identification. The proposed model is verified by showing a good agreement with the experimental data. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)