Duality results and regularization schemes for Prandtl--Reuss perfect plasticity

We consider the time-discretized problem of the quasi-static evolution problem in perfect plasticity posed in a non-reflexive Banach space and we derive an equivalent version in a reflexive Banach space. A primal-dual stabilization scheme is shown to be consistent with the initial problem. As a consequence, not only stresses, but also displacement and strains are shown to converge to a solution of the original problem in a suitable topology. This scheme gives rise to a well-defined Fenchel dual problem which is a modification of the usual stress problem in perfect plasticity. The dual problem has a simpler structure and turns out to be well-suited for numerical purposes. For the corresponding subproblems an efficient algorithmic approach in the infinite-dimensional setting based on the semismooth Newton method is proposed

Some results on quasistatic evolution problems for unidirectional processes

The present thesis is devoted to the study of some models of quasistatic evolutions for materials, in the presence of unidirectional phenomena, such as damage and fracture. In particular, these models concern the coupling between damage and plasticity, and the growth of brittle and cohesive fractures in antiplane linearized elasticity