Open Access

ARTICLE

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

Chein-Shan Liu¹

1 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 q₀^a and q₀^b; the first q₀^a controls the on/off switch of plasticity, and the second q₀^b 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 q₀^b = 0, q₀^b = q₀^a and q₀^b ≠ q₀^a. 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.

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