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Computational Applications of the Poincaré Group on the Elastoplasticity with Kinematic Hardening

Chein-Shan Liu1
Department of Mechanicaland Mechatronic Engineering, Taiwan Ocean University, Keelung, Taiwan, E-mail: csliu@mail.ntou.edu.tw

Computer Modeling in Engineering & Sciences 2005, 8(3), 231-258. https://doi.org/10.3970/cmes.2005.008.231

Abstract

Using a group-theoretical approach in the Minkowski space we explore kinematic hardening rules from a viewpoint of the Poincaré group. The resultant models possess two intrinsic times q0a and q0b; the first q0a controls the on/off switch of plasticity, and the second q0b controls the pace of back stress during plastic deformation. We find that some existent kinematic hardening rules, including the modifications from the Armstrong-Frederick kinematic hardening rule, can be categorized into type I, type II and type III, which correspond respectively to q0b = 0, q0b = q0a and q0bq0a. Based on group properties, the numerical computations of models' responses are derived, which can automatically update the stress points located on the yield surface at every time step without needing of iteration, and some examples are plotted to show models' behaviors.

Keywords

Elastoplasticity, kinematic hardening rule, Poincaré group, numerical computation, Minkowski space

Cite This Article

Liu, C. (2005). Computational Applications of the Poincaré Group on the Elastoplasticity with Kinematic Hardening. CMES-Computer Modeling in Engineering & Sciences, 8(3), 231–258.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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