Micromechanics-based elasto-plastic–damage energy formulation for strain gradient solids with granular microstructure

Approaches aimed at handling dissipation occurring in non-conservative physical systems are extensively discus- sed in the scientific literature. Damage and plasticity are complex dissipative phenomena which are especially interesting for the engineering community, because they are occurring in many different materials employed in engineering applications, like structural steel and concrete. The presentation will be devoted to the development of a continuum theory for materials having granular microstructure and accounting for some dissipative phenomena like damage and plasticity. The continuum description is constructed by means of purely mechanical concepts, assuming expressions of elastic and dissipation energies as well as postulating a hemi-variational principle, wi- thout incorporating any additional postulate like flow rules. Granular micromechanics is connected kinematically to the continuum scale through Piola’s ansatz. Numerical experiments have been performed to investigate the applicability of the model. Cyclic loading–unloading histories have been considered to elucidate the material hysteretic features of the conti- nuum, which emerge from simple grain–grain interactions. The competition between damage and plasticity, each having an effect on the other, has been assessed. Furthermore, the evolution of the load-free shape is shown not only to quantify the plastic behaviour, but also to make tangible the point that, in the proposed approach, plastic strain is found to be intrinsically compatible with the existence of a placement function.