A hybrid potential of mean force approach for simulation of fracture in heterogeneous media

Abstract

Material heterogeneity at small scales is a key driver of material’s effective macroscopic properties and fracture response. We present a hybrid energy-based approach based on a potential of mean force formulation of lattice element method for reliable and efficient modeling of fracture and crack propagation in heterogeneous materials. The proposed framework rests on direct application of the Griffith fracture criteria and removes material points to create fracture surfaces in energetically favorable directions. Computational efficiency is achieved through a probing of high energy bonds and quasi-static relaxation leading to near global imposition of the energy-based criteria for crack path resolution. We validate the proposed hybrid approach against results in literature and use it to examine fracture response of defective and layered materials. For layered materials with fracture energy heterogeneity, the effective toughness is shown to be the maximum of fracture energies of layers irrespective of their volume fraction and the direction of crack propagation. For layered materials with elastic modulus heterogeneity, the maximum energy release rate occurs when the crack approaches the compliant-stiff interface from within the compliant phase. We examine the scaling of fracture toughness with modulus contrast, the link to volume fraction of the layers and the relationship between toughness anisotropy and the gradient of elastic modulus heterogeneity, offering insights with potential to inform the design of materials for fracture.