Granular-based continuum elasto-plastic–damage variational formulation for strain gradient solids

This work is devoted to the presentation of a continuum theory [1,2] for materials having granular microstructure [3,4]. It accounts for tension–compression asymmetry of grain interactions and for dissipative phenomena like damage and plasticity. The continuum description is constructed by assuming expressions of elastic and dissipation energies as well as postulating a hemi-variational principle. Granular micromechanics is connected kinematically to the continuum scale through Piola’s ansatz. Karush–Kuhn–Tucker (KKT)-type conditions, providing evolution equations for damage and plastic variables associated with grain–grain interactions, are derived solely from the fundamental postulates. Numerical experiments have been performed to investigate the applicability of the model. Results show: (i) damage and plastic induced anisotropy evolution including the emergence of a type of chiral behavior. (ii) formation of finite localization zones. (iii) loading–unloading histories have been considered to elucidate the material hysteretic features of the continuum. (iv) The interaction between damage and plasticity, each having an effect on the other, shows the fatigue behavior of the material. (v) A particular expression for the dissipation energy results in numerical simulations of the experimental behavior of the Ultra High Performance Concrete. (vi) Emergence of the critical state of a granular assembly has been derived with a systematic parametric analysis.