Damage Models for Micromorphic Continuum

Numerous materials, although they appear macroscopically homogeneous, usually present a heterogeneous microstructure that directly influences the structural behavior. The phenomenological approach followed by the classical continuum mechanics does not individually accounts for this influence, which can be significant, for example, in cases where the structure or the specimen under analysis is small compared to its microstructure or when the material media has a complex microstructure. Within the framework of continuum mechanics, so-called generalized continuum theories are particularly suited to deal with the above issues incorporating the microstructural behavior on the formulation. The micromorphic theory is included in this general class of generalized continua and, more specifically, in the group that incorporates additional degrees of freedom to the material particles.Another aspect of generalized continua is its ability to address the issue of localization in quasi-brittle materials modeled as elastic-degrading media as a result of its non-local character. In order to allow the representation of quasi-brittle media with the micromorphic continuum theory, this work presents a formulation for scalar-isotropic damage models for a micromorphic continuum in the constitutive models framework of the INSANE system, initially conceived for classical media and later expanded for the micropolar continuum. This implementation is based on the tensorial format of a unified constitutive models formulation and homogenization techniques to obtain the micromorphic constitutive relations.