Multifractal fracture-toughness properties of brittle heterogeneous materials

This paper documents a study of novel fracture-toughness properties of brittle heterogeneous materials. Through simulations of the rupture process based on a lattice discretization of the material, the spatial variation of dissipated energy due to fracture is evaluated. Under certain conditions, its distribution is characterized by a multifractal spectrum f (α). Importantly, f (α) depends not only on the initial heterogeneity present in the material but also on the nature of the externally applied load. This provides a renewed load-path-dependent definition of fracture toughness material properties. It avoids the difficulties associated with 'traditional' continuum/fracture mechanics definitions where the macroscopic fracture mode must be known a priori.