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Lie Group Symmetry Applied to the Computation of Convex Plasticity Constitutive Equation

C.-S. Liu1,2, C.-W. Chang1
Department of Mechanical and Mechatronic Engineering, Taiwan, Ocean University, Keelung, Taiwan.
Corresponding author. E-mail:

Computer Modeling in Engineering & Sciences 2004, 6(3), 277-294.


This paper delivers several new types of representations of the convex plasticity equation and realizes them by numerical discretizations. In terms of the Gaussian unit vector and the Weingarten map techniques in differential geometry, we prove that the plastic equation exhibits a Lie group symmetry. We convert the nonlinear constitutive equations to a quasilinear equations system X = AX, X ∈ Mn+1, A ∈ so(n,1) in local. In this way the inherent symmetry of the constitutive model of convex plasticity is brought out. The underlying structure is found to be a cone in the Minkowski space Mn+1 on which the proper orthochronous Lorentz group SOo(n,1) left acts. Based on the group properties some numerical methods are developed, which together with a post-projecting method can update the stress points on the yield surface at every time increment.


Computational plasticity, convex plasticity, Lorentz group, consistent scheme.

Cite This Article

Liu, C., Chang, C. (2004). Lie Group Symmetry Applied to the Computation of Convex Plasticity Constitutive Equation. CMES-Computer Modeling in Engineering & Sciences, 6(3), 277–294.

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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