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Towards variational constitutive updates for finite strain plasticity models based on non‐associative evolution equations
Author(s) -
Mosler Jörn
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910134
Subject(s) - constitutive equation , associative property , plasticity , mathematics , finite strain theory , variational principle , computer science , calculus of variations , finite element method , mathematical analysis , physics , pure mathematics , structural engineering , engineering , thermodynamics
In this contribution, first steps towards variational constitutive updates for finite strain plasticity theory based on non‐associative evolution equations are presented. These schemes allow to compute the unknown state variables such as the plastic part of the deformation gradient, together with the deformation mapping, by means of a fully variational minimization principle. Therefore, standard optimization algorithms can be applied to the numerical implementation leading to a very robust and efficient numerical implementation. Particularly, for highly non‐linear, singular or nearly ill‐posed physical models like that corresponding to crystal plasticity showing a large number of possible active slip planes, this is a significant advantage compared to standard constitutive updates such as the by now classical return‐mapping algorithm. While variational constitutive updates have been successfully derived for associative plasticity models, their extension to more complex constitutive laws, particularly to those featuring non‐associative evolution equations, is highly challenging. In the present contribution, a certain class of non‐associative finite strain plasticity models is discussed and recast into a variationally consistent format. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)