**Rate independent
variational**

**and**

**Quasivariational****
inequalities in elastoplasticity**

Martin Brokate

Variational formulations are commonly used for problems in mechanics, for mathematical analysis as well as for numerical approximations (e.g., finite elements). Elastoplastic constitutive laws possess the property of rate independence, and the variational inequality constitutes the proper mathematical setting which encompasses the interplay of elastic and plastic deformation. The admissible stresses form a closed convex subset of the stress space. In most cases of practical importance, the set of admissible stresses is not fixed, but depends on the loading history. In some cases, this varying set can be transformed to a fixed set, but if this is not possible, the more general and more difficult setting of a quasivariational inequality has to be considered. We present in particular some new results concerning existence and uniqueness of such a quasivariational inequality.