Crack propagation in quasi-brittle two-dimensional isotropic lattices

Materials with cellular structure are gaining prominence in recent years due to improvements in production processes, that enable the manufacture of new materials, and biomechanics, that requires mechanical analysis of cellular structures such as bones. The possibility to use the Fracture Mechanics tools developed for the continua to the fracture of cellular materials is analyzed in the present paper. As proposed by Maiti et al. the fracture toughness of cellular solids can be obtained through two procedures: taking into account the stress at crack tip or the fracture toughness of the base material. Both procedures are analyzed and the equivalent R-curve and a cohesive law is obtained in function of the cell size and structure morphology. A critical truss length exists from which crack propagation goes from being governed by the energy dissipated to being governed by the stress field.