Modeling anisotropic damage in elasto-plastic materials with structural defects

The paper deals with models for elasto-plastic materials with continuously distributed micro defects (micro cracks, micro voids, extra-matte), compatible with the principle of imbalance of the free energy. As the plastic behaviour and the damage are essentially irreversible, the behaviour of elasto-plastic materials with damaged microstruc- ture is described in terms of specific differential geometry elements which characterize the internal mechanical state. In the models proposed in this paper, the key point is the symmetric tensorial damage variable, which is a measure of non-metricity of the geom- etry associated with elasto-plastic material with damaged structure. The free energy density is supposed to be dependent not only by the elastic strain but also on the the Bilby’s type connection, which generates through the attached torsion, the dislocation density. The tensorial measure of the damage as well as its gradient, which generate the quasi-dislocation density, are involved in the expression of the free energy density. The evolution equations for the plastic distortion and tensorial damage variable are derived to be compatible with the reduced dissipation inequality. A rate independent non-local elasto-plastic model coupled with damage has been proposed