Fracture simulation using a discrete triangular element

A triangular element constructed from constant strain triangles with nodes along its sides is developed for the simulation of fracture. Fracture is captured through a constitutive softening-fracture law at the interface nodes. The material within the triangular unit remains elastic. The plastic displacement at the interface nodes represents the relative crack opening displacement, which are related to the conjugate inter-nodal force by the appropriate softening relationship. The path-dependent softening behaviour is solved in non-holonomic rate form based on a quasi-prescribed displacement formulation. At each event in the loading history all solutions are obtained and the critical path with the minimum second order work; is adopted. All solutions are obtained using an enumerative procedure based on the observation that the solution of an LCP can be found by an exhaustive exploration of a binary tree. The classical three point bending and two notch tensile tests are simulated and compared with other published results.