Stability and Bifurcation in Nonlinear Mechanics

Abstract

Analysis of stability and bifurcation is studied in nonlinear mechanics with mechanisms of dissipation: plasticity, damage, fracture. With introduction of a set of internal variables, this framework allows a systematic description of the material behavior via two potentials: the free energy and the potential of dissipation. For standard generalized materials, internal state evolution is governed by a variational inequality depending on the mechanism of dissipation. This inequality is obtained through energetic considerations in an unified description based upon energy and driving forces associated with internal variable evolution. This formulation provides criterion for existence and uniqueness of the system evolution. Examples are presented for plasticity, fracture and damaged materials.