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Geometrically non‐linear anisotropic inelasticity based on fictitious configurations: Application to the coupling of continuum damage and multiplicative elasto‐plasticity
Author(s) -
Menzel A.,
Steinmann P.
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.662
Subject(s) - multiplicative function , plasticity , continuum mechanics , dissipation , equivalence (formal languages) , eulerian path , mathematics , anisotropy , coupling (piping) , classical mechanics , lagrangian , physics , mathematical analysis , pure mathematics , engineering , mechanical engineering , quantum mechanics , thermodynamics
The objective of this contribution is the formulation and algorithmic treatment of a phenomenological framework to capture anisotropic, geometrically non‐linear inelasticity. In addition to the intermediate configuration of multiplicative elasto‐plasticity, we further introduce two microscopic configurations of Lagrangian and Eulerian type which characterize the so‐called fictitious undamaged material. This kinematical framework enables us to apply two well‐established postulates based on standard terminology in non‐linear continuum mechanics. Concerning the free energy function, the postulate of strain energy equivalence is adopted and in view of the plastic dissipation potential the concept of effective stress is a natural outcome of the underlying kinematical assumptions. Finally, we focus on the integration technique for the class of obtained evolution equations and present numerical examples for a prototype model to underline the applicability of the proposed framework. Copyright © 2003 John Wiley & Sons, Ltd.