Mathematics

 The aim of the course is to present recent results in the mathematical theory of quasistatic crack growth in elastic materials, in the context of finite elasticity. In the first part of the course we will discuss the model of finite elasticity and the existence of static equilibria basing on variational methods. In the second part, we will introduce fracture and the functional spaces needed to keep track of discontinuities in the deformations. We will show the existence of quasistatic evolutions featuring a global stability and an energy-dissipation balance, in the context of rate-independent processes. A special focus will be given to the modelling of non-interpenetration of matter.