Computational Mechanics

, Volume 60, Issue 5, pp 703–707 | Cite as

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

  • M. B. RubinEmail author
  • P. Cardiff


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.


Elastic distortional deformation Evolution equations Finite deformation Plasticity 



This research was partially supported by MB Rubin’s Gerard Swope Chair in Mechanics. Also, MB Rubin acknowledges the University College Dublin for graciously hosting him during part of his sabbatical leave from Technion. In addition, financial support is gratefully acknowledged from Bekaert through the University Technology Centre (UTC), and the Irish Centre for Composites Research (IComp). Additionally, the authors wish to acknowledge the DJEI/DES/SFI/HEA Irish Centre for High-End Computing (ICHEC) for the provision of computational facilities and support.


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© 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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