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arXiv · 1311.6792

Analysis of some basic approaches to finite strain elasto-plasticity in view of reference change

A. V. Shutov·J. Ihlemann
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Abstract

There is a large variety of concepts used to generalize the classical Prandtl-Reuss relations of infinitesimal elasto-plasticity to finite strains. In this work, some basic approaches are compared in a qualitative way with respect to a certain invariance property. These basic approaches include the additive hypoelasto-plasticity with corotational stress rates, additive plasticity in the logarithmic strain space, and multiplicative hyperelasto-plasticity. The notion of weak invariance is introduced in this study. Roughly speaking, a material model is weakly invariant under a certain transformation of the local reference configuration if this reference change can be neutralized by a suitable transformation of initial conditions, leaving the remaining constitutive relations intact. We analyse the basic models in order to find out if they are weakly invariant under arbitrary volume-preserving transformations of the reference configuration. It is shown that the weak invariance property corresponds to a generalized symmetry which provides insights into underlying constitutive assumptions. This property can be used for a systematic study of different frameworks of finite strain elasto-plasticity. In particular, it can be used as a classification criterion.

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A. V. Shutov, J. Ihlemann. 2013-11-13. Analysis of some basic approaches to finite strain elasto-plasticity in view of reference change. https://doi.org/10.1016/j.ijplas.2014.07.004

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