A damage growth criterion for anisotropic damage models motivated from micromechanics

The field of continuum damage mechanics addresses mathematical models for the degradation of the mechanical properties of engineering materials, in particular for softening effects. It is therefore reasonable to define what 'degradation of properties' in general means, in order to test if a given damage model actually leads to a degradation of the material properties. To this end, a criterion for damage growth is proposed for the class of phenomenological anisotropic damage models with internal variables. The criterion is motivated by micromechanical investigations of crack networks and pores, being the two main microscopic damage mechanisms. It is then shown that the behavior of a given damage model can indeed become spurious, if it does not respect the aforementioned damage growth criterion. For example the violation of the criterion by a given elastic-brittle damage model is shown to be equivalent to an increase of the elastic stiffness for certain strain states, which is basically the opposite of stiffness 'degradation'. Furthermore, it is illustrated that the (possibly anisotropic) growth of pores in ductile damage can be expected to also result in an elastic stiffness degradation and a shrinkage of the yield surface on the macroscale.