Rate-independent damage processes in nonlinear elasticity

Damage of an elastic body undergoing large deformations by a "hard-device" loading possibly combined with an impact (modeled by a unilateral frictionless contact) of another, ideally rigid body is formulated as an activated, rate-independent process. The damage is assumed to absorb a specific and prescribed amount of energy. A solution is defined by energetic principles of stability and balance of stored and dissipated energies with the work of external loading, realized here through displacement on a part of the boundary. Rigorous analysis by time discretization is performed.