Journal of Theoretical
and Applied Mechanics

35, 3, pp. 551-575, Warsaw 1997

A kind of unification in continuum mechanics

Jan Saczuk
The aim of this paper is to propose a kind of unification within the framework of continuum mechanics theories, by means of which the inelastic behaviour of solids is modelled. In this approach deformation (kinematics) of the continuum and its substructure is described in terms of a structure of the Finsler bundle. This new theoretical background, being physically justified, is used for formulation of an alternative continuum description of a solid behaviour. The additive decomposition of the total deformation gradient is defined with no additional assumptions like: intermediate stress-free configuration, yield rule, hardening and/or softening laws. This leads to new strain measures which are both aniso-tropic and internal-variable-dependent. The rate-independent example of a solid deformation is included to show that this approach requires no extra theories for description of the residual state, softening and hardening phenomena.
Keywords: Finsler geometry; continuum with microstructure; inelastic deformation