Continuum damage model for strain gradient materials with applications to 1D examples

In complex materials there exist different, often independent, mechanisms for the evolution of anelastic phenomena at the micro- and at the macroscale. Consequently, gradient plasticity has been introduced for a large variety of non-local materials. In a similar way, continuum damage has been extended to micromorphic and other non-local models, introducing internal damage variables and their gradient. In the paper is proposed a new continuum damage model for strain gradient materials characterized by two independent damage internal variables, each evolving with its own law. In this way, no additional field equation for the damage variable is needed. The model is intended to be used for metamaterials. Some important characteristics of the model are analysed with numerical analyses of a 1D example. In particular, the ability of the model to prevent strain localization is discussed.