Variational and hemivariational inequalities in mechanics of elastoplastic, granular media, and quasibrittle cracks

Abstract

This contribution is devoted to the mathematical theory of elastoplastic and granular solids as well as the quasibrittle fracture of nonlinear cracks. Basic variational and hemivariational inequalities describing nonlinear phenomena due to plasticity, internal friction, interfacial interaction, and alike dissipative physics are outlined from the point of view of nonsmooth and nonconvex optimization. Primary results of the nonlinear theory and its application to solid mechanics are surveyed.