Multiscale phase-field approach for investigation of anisotropic fracture properties of architected materials

Abstract

We propose a computational approach to determining the direction-dependent fracture toughness of architected materials. Using the principles of multiscale mechanics and phase-field modelling of fracture, our proposition enables straightforward determination of the macroscopic toughness of the homogenized material. The most important feature of our computational scheme is the loading arrangement which ensures the crack propagation along a macroscopic straight line in the same direction as the initial notch, irrespective of the material’s orientation. Forcing the crack propagation in a specific direction, we extract the toughness of the homogenized material in that direction by utilizing the equivalence of dissipation in micro and macro scales. Diffused representation of crack, both in micro and macro scales, through a phase-field formalism has been adopted to simulate crack propagation and establish the necessary expression for quantifying direction-dependent macroscopic toughness. We verify the capability of the proposed approach by computing the fracture toughness of a brittle layered media and comparing the result with that available in the literature. We subsequently apply the algorithm to investigate the fracture behaviour of brittle architected lattice materials of two types– a material with an array of circular holes and triangular lattice. The nature of fracture anisotropy and the effect of relative density on fracture behaviour of these materials, as derived through the present technique, are highlighted.