Calculus of Variations and Geometric Measure Theory

G. A. Francfort - A. Giacomini

Small Strain Heterogeneous Elasto-Plasticity Revisited

created by giacomini on 28 Jun 2011
modified on 15 Nov 2012


Published Paper

Inserted: 28 jun 2011
Last Updated: 15 nov 2012

Journal: Comm. Pure Appl. Math.
Volume: 65
Pages: 1185-1241
Year: 2012
Doi: 10.1002/cpa.21397


The elasto-plastic quasi-static evolution of a multi-phase material -- a material with a pointwise varying yield surface and elasticity tensor, together with interfaces between the phases -- is revisited in the context of conservative globally minimizing movements. Existence is shown, and classical evolutions are recovered under natural constraints on the plastic dissipation potential. Special attention is paid to the interfaces where the correct dissipation has to be enforced on the interfaces. Further, the evolution is shown to be a limit of that obtained for a model with linear isotropic hardening as the hardening becomes vanishingly small. The duality between plastic strains and admissible stresses is also revisited for Lipschitz boundaries and its role in deriving a classical evolution is circumscribed.