The influence of deformation path on adaptation process of a solid

Abstract

The idea of a criterion of adaptation process of a body, accounting for the influence of deformation path on the material properties of the body, is proposed. A change of the deformation path, realized either through the change of slip systems and/or by changing external loads, is analyzed within the Finslerian description of the solid behaviour. In this continuum model no yield rule and no intermediate configuration are assumed to exist, and the transition from micro- to macroscales is natural. This approach makes possible the description of yielding, softening, hardening and localization of solids within the unified concept. A shakedown theorem, based on the Finslerian continuum model, is formulated within the theory of differential inequalities. The presented theorem, in which a definite amount of the total strain energy comes into play, has no counterparts in the available literature. It generalizes the classical approaches to the adaptation problems by including arbitrary deformations and material nonlinearities.