Continuum model of microstructure induced softening for strain gradient materials

Gradient plasticity has been introduced to predict localization bands induced by softening or damage, and has been extended to micromorphic models used for materials with microstructure and scale effects. Motivated by the consideration that in complex materials there may exist different mechanisms for the evolution of anelastic deformation at the small and at the large scale, and that they may interact, in the paper a model of second gradient material with two different evolution laws for the macroscopic and for the microscopic plastic strain is proposed, the latter related to the presence of second gradient deformation. The model is intended to be used for metamaterials, and its relevant properties can be obtained from an homogenization analysis at the microlevel.