Lorentz group SO0(5, 1) for perfect elastoplasticity with large deformation and a consistency numerical scheme
Journal
International Journal of Non-Linear Mechanics
Journal Volume
34
Journal Issue
6
Pages
1113-1130
Date Issued
1999
Author(s)
Liu C.-S.
Abstract
How to effectively deal with non-linearity and accurately fulfill the consistency condition is essential for modeling and computing in plasticity. Utilizing the concepts of two phases and homogeneous coordinates, we obtain a linear representation of a constitutive model of perfect elastoplasticity with large deformation, and, furthermore, a linear irreducible representation, which contains a five-order spin tensor. The underlying vector space is found to be the projective realization of a composite space resulting from a surgery on Minkowski spacetime double-struck M sign 5 + 1. The irreducible representation in the vector space admits of the projective proper orthochronous Lorentz group PSO0(5, 1) in the on (or elastoplastic) phase and the special Euclidean group SE(5) in the off (or elastic) phase. The input path dictates symmetry switching between the two groups. Based on such symmetry a numerical scheme is devised which preserves the consistency condition for every time step. The consistency scheme is shown to be stabler, more accurate, and more efficient than the current numerical schemes developed directly based upon the model itself, because the new scheme preserves the internal symmetry SO0(5, 1) of the model in the on phase so as to locate the stress point automatically on the yield surface at each time step without iterations at all. © 1999 Elsevier Science Ltd. All rights reserved.
Subjects
Consistency scheme; Elastoplasticity; Irreducible representation; Large deformation; Lorentz group
SDGs
Type
journal article