05.11.2018 14:00 Gianluca Orlando:Fatigue effects in elastic materials with variational damage modelsMI 02.10.011 (Boltzmannstr. 3, 85748 Garching)

In this talk I will present an existence result concerning quasistatic evolutions for a family of gradient damage models which take into account fatigue, that is the process of weakening in a material due to repeated applied loads. The main feature of these models is the fact that damage is favoured in regions where the cumulation of the elastic strain (or other relevant variables, depending on the model) is higher. The existence of a quasistatic evolution is proven via a vanishing viscosity approach based on two steps: first let the time-step of the time-discretisation and later the viscosity parameter go to zero. As the time-step goes to zero, one finds approximate viscous evolutions; then, as the viscosity parameter goes to zero, one finds a rescaled approximate evolution satisfying an energy-dissipation balance. The result is based on a work in collaboration with Roberto Alessi and Vito Crismale.