CHARACTERIZATION OF ANISOTROPIC HARDENING MATERIAL, QUASI-STATIC BEHAVIOUR AS A LIMIT PROCESS OF A DYNAMICAL ONE

Quasi-static deformation can be seen as a limit case of the dynamic deformation, corresponding to low speeds and low inertial forces. We formulate some problems modelling the local behavior of a plastic material with hardening, following a Prendtl-Reuss law. The flow process of material is revealed by translation in the direction shown by deformation, using an absolutely continuous guiding function. Directional linear hardening, which is similar to Bauschinger's effect in metals, is characterized by a guiding factor. The possibility of choice of a plastic strain component for the mechanical system with hardening requires an algebraic factorization of the space of processes. We obtain an existence and uniqueness result. In this context there exist an admissible plastic strain rate, by selection, and a permissible elastic stress for a sweeping process.