Damage integration in the strain space

The focus is on isotropic elastodamaging (softening) materials, where the damage parameter is expressed as a function of the total strain. By integrating the mechanical work in the strain space along a stepwise holonomic loading history, an incremental strain energy is obtained. A coaxiality condition for the incremental strain energy to be potential is identified, and its implications on the associativity of the damage evolution are discussed. Under some hypotheses, the increment of the mechanical work is shown to be minimum along strain radial paths. These results are used to construct a multifield variational framework supporting finite element (nonlocal) formulations.