Prediction of multiscale crack propagation in anisotropic microstructures by using an efficient cohesive/bulk homogenization scheme

In recent years, several enhanced homogenization approaches have been proposed with the aim of overcoming the limitations of classical first-order homogenization techniques in correctly capturing the softening behavior of quasi-brittle composite structures. However, most of these approaches, such as continuous/discontinuous homogenization schemes, are formulated within FE2-like methods, and therefore they usually require very large computational efforts. In the present work, a more efficient hierarchical cohesive/bulk homogenization approach is proposed for the prediction of multiscale crack propagation in anisotropic microstructures. Such an approach is intended to be used in combination with a Diffuse Interface Model (DIM) at the macroscopic scale, in which both bulk and cohesive macro-elements are equipped with overall anisotropic constitutive laws, both derived starting from a nonlinear homogenization performed on a suitably defined Repeating Unit Cell (RUC) subjected to periodic boundary conditions. As the main novelty point, an ad-hoc numerical procedure is proposed to extract a microscopically informed cohesive Traction-Separation Law (TSL) “on-the-fly”, i.e., during the crack propagation analysis at the macroscopic level. The proposed model is then applied to the multiscale simulation of crack propagation in a porous heterogeneous beam chosen as a benchmark example. Finally, the accuracy and computational efficiency of the multiscale simulations have been shown by means of suitable comparisons with direct simulations performed on a fully meshed model.