Internal Symmetry in the Constitutive Model of Perfect Elastoplasticity
Resource
International Journal of Non-Linear Mechanics 35: 447-466
Journal
International Journal of
Journal Issue
Non-Linear
Pages
447-466
Date Issued
2000
Date
2000
Author(s)
Liu, Chein-Shan
Abstract
Internal symmetry in the constitutive model of perfect elastoplasticity is investigated here. Using homogeneous coordinates, we convert the non-linear model to a linear system. In this way the inherent symmetry in the constitutive model of perfect elastoplasticity (in the on phase) is brought out. The underlying structure is found to be the cone of Minkowski spacetime Mn+1 on which the proper orthochronous Lorentz group SO0(n, 1) left acts. When the plasticity mechanism is shut off by the input path, the internal symmetry is switched to a translation group T(n) acting on the closed disc Dn of Euclidean space En. Based on the group properties a Cayley transformation is developed, which updates the stress points to be automatically on the yield surface at every time increment. These results (and their generalizations to more sophisticated models) are essential for computational plasticity. As an example, the results calculated using the group-preserving scheme and the exact constitutive solutions for a rectilinear path are compared.
Type
journal article
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