Elastic degradation models for the micromorphic continuum

Abstract

Numerous applications of generalized continua theories have been proposed mainly due to their regularization properties when applied to strain localization problems. This characteristic is directly correlated to the nonlocal feature of generalized media, wherein the material microstructural behavior is incorporated into the continuum formulation. The micromorphic theory poses as the most general theory in this class of generalized theories through the consideration of nine additional degrees of freedom embedded in each material particle. In order to allow the application of the micromorphic theory associated to damage models, extending its regularization properties to different constitutive models, this work presents an extension of classical elastic-degrading damage models for the micromorphic theory focused on scalar-isotropic models. To guarantee conformity to a constitutive models framework implemented for the classical continuum, a compact tensorial formulation is proposed, allowing the application, for the micromorphic theory, of theoretical and numerical resources already defined for the classical theory. A homogenization strategy is also employed to obtain the micromorphic constitutive relations through the consideration of a Cauchy continuum in the microscale, allowing nonlinear analysis of micromorphic media with only the definition of the material parameters of the classical continuum.