On Energy Release Rates and Configurational Forces for Interfacial Propagating Cracks: A Lattice Approach With a Brittle Erosion Technique

Abstract

A numerical 2D lattice approach with an erosion algorithm is employed to analyze bimaterial interface fracture quantities in brittle heterogeneous materials in the context of linear elastic fracture mechanics (LEFM). The concept of configurational force is elucidated and the importance of nodal configurational changes in a mesh where no stress–strain analyses are needed is investigated. Three fracture problems, i.e., an infinite panel with a bi-material interface crack, a double-lap shear test, and a prenotched four-point bending masonry beam are then considered. Validated by analytical solutions, the lattice model uses two distinct postprocessing approaches to derive the energy release rates and configurational forces directly at bimaterial interface crack tips. While the first method takes advantage of the change of the lattice mesh's global stiffness matrix before and after crack growth without any stress–strain calculations to obtain crack tip driving forces, the second approach analyzes the configurational forces opposing the crack tip motion using the Eshelby stress tensor and local force balance law in cracked and heterogeneous domains. It is demonstrated that the discrete material forces at crack tips are closely equal to the tip driving forces for the three fracture problems, confirming that the lattice is an appropriate numerical tool to analyze fracture properties of evolving interface cracks. Satisfying C1 continuity by including rotational displacements for frame struts, there is also no need for the lattice to update interior computational points in the mesh to eliminate spurious material forces away from the tip.