On the role of the Finsler geometry in the theory of elasto-plasticity

Abstract

The one-to-one correspondence of the physical (yield surface) and geometric (indicatrix) objects is used to describe, on a Finsler bundle, geometric aspects of the elasto-plastic behaviour of a solid. The arrangement of the paper and the choice of basic topic are intended to present a new consistent internal-variable theory of elasto-plastic solids. It is based on non-Euclidean premises which allow a clear theoretical separation of elasto-plastic deformation process of the solid within the Finsler geometry. The variational arguments for a given Lagrangian functional defined on the Finsler bundle, and an assumed one-parameter family of transformations of both the independent and dependent variables, are used to define a set of equations of elasto-plastic problem. The Weierstrass condition is specified to the Clausius-Duhem inequality for the mechanical side of the elasto-plastic behaviour. A reinterpretation of the classical constitutive relations in terms of Finsler's geometry is presented. Attention is restricted throughout to the theoretical considerations.