Strain localization analysis in micromorphic media from macro and microscale perspectives

Resumo

The study of failure conditions and failure modes at the material level within classical continua has been extensively studied in terms of a localization analysis, where discontinuous failure initiates when the second-order localization tensor or its symmetric counterpart becomes singular. Strain localization, characterized by the formation of jumps in field variables across a singularity surface, serves as a threshold for the introduction of discontinuities when damage and failure are approached from a continuous-discontinuous perspective. In these models, a continuous model simulates micro-cracking and, upon localization, strong discontinuities are introduced to simulate crack formation. Considering the multiscale nature of deformation and failure processes, specially in microstructured materials, extending continuous-discontinuous models to generalized continuum frameworks are of interest. However, the micromorphic continuum, in particular, is well know for its regularization properties due to its high level of generalization and non-local formulation. In this study, a localization indicator that overcomes the regularization effects of the micromorphic continuum is presented, enabling the identification of both the onset and direction of strong discontinuities. The micromorphic acoustic tensor is studied from macro- and microscale perspectives in an elastic degradation framework. Numerical investigations are performed using implementations developed within the open-source software INSANE.