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Computational Mechanics

, Volume 60, Issue 5, pp 703–707

# Advantages of formulating an evolution equation directly for elastic distortional deformation in finite deformation plasticity

Letter

## Abstract

Simo (Comput Methods Appl Mech Eng 66:199–219, 1988) proposed an evolution equation for elastic deformation together with a constitutive equation for inelastic deformation rate in plasticity. The numerical algorithm (Simo in Comput Methods Appl Mech Eng 68:1–31, 1988) for determining elastic distortional deformation was simple. However, the proposed inelastic deformation rate caused plastic compaction. The corrected formulation (Simo in Comput Methods Appl Mech Eng 99:61–112, 1992) preserves isochoric plasticity but the numerical integration algorithm is complicated and needs special methods for calculation of the exponential map of a tensor. Alternatively, an evolution equation for elastic distortional deformation can be proposed directly with a simplified constitutive equation for inelastic distortional deformation rate. This has the advantage that the physics of inelastic distortional deformation is separated from that of dilatation. The example of finite deformation $$\hbox {J}_{2}$$ plasticity with linear isotropic hardening is used to demonstrate the simplicity of the numerical algorithm.

## Keywords

Elastic distortional deformation Evolution equations Finite deformation Plasticity

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## Copyright information

© Springer-Verlag GmbH Germany 2017

## Authors and Affiliations

1. 1.Faculty of Mechanical EngineeringTechnion - Israel Institute of TechnologyHaifaIsrael
2. 2.School of Mechanical and Materials EngineeringUniversity College DublinDublin 4Ireland

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