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Article

Horák, Martin ; Jirásek, Milan
An extension of small-strain models to the large-strain range based on an additive decomposition of a logarithmic strain. (English). In: Chleboun, J., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 3-8, 2012. Institute of Mathematics AS CR, Prague, 2013. pp. 88-93
MSC: 74C05, 74C15
Keywords:
elasto-plasticity; damage evolution; non-local models; generalized stain measures; logarithmic strain
Summary:
This paper describes model combining elasticity and plasticity coupled to isotropic damage. However, the conventional theory fails after the loss of ellipticity of the governing differential equation. From the numerical point of view, loss of ellipticity is manifested by the pathological dependence of the results on the size and orientation of the finite elements. To avoid this undesired behavior, the model is regularized by an implicit gradient formulation. Finally, the constitutive model is extended to the large-strain regime. The large strain model is based on the additive decomposition of the logarithmic strain and preserves the structure of the small-strain theory.
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