Coupled Micromechanics -embedded strong discontinuity model for quasi-brittle fracture: a variational appraisal

Recently, a variational principle [1, 2] has been exploited as a means to couple rigorously Computational Continuum-Micromechanics [3, 4] and the Embedded Strong Discontinuity approach [5], in a seamless fashion. The method enables minimal remeshing at the global-scale upon macroscopic fracture, while directional diffuse microcracking can evolve at the material-scale. Macrocrack nucleation occurs upon substantial development of directional microcracking. In this regard, macrocrack detection is underpinned by the philosophy of microcracks coalescing onto sharp macrocracks [6]. Element-wise treatment of macrocrack evolution, opposed to traditional global treatment [7], is turned possible by means of finding the optimal energetic state including micro and macro components simultaneously, which allows to condensate quasi-statically additional macrocrack dofs. Such methodology has been successfully tested for multiscale fracture propagation analysis in cementitious composites. Attention is given to the variationally-consistent nature of the numerical framework, which enforces weakly traction continuity along embedded macrocracks within the Micromechanical continua, and provides a least-energy solution. Such rigorous variational appraisal has proved to be pivotal for developing these new theories on multiscale fracture mechanics.