Numerical simulation of quasibrittle fracture in concrete

A triangular unit, constructed from constant strain triangles with nodes along its sides and not at the vertex, is developed for the simulation of fracture in quasibrittle materials. Fracture is modelled through a constitutive softening–fracture law at the interface nodes, with the material within the triangular unit remaining linear elastic. The inelastic displacement at an interface node represents the crack opening, which is related to the conjugate inter-nodal force by the appropriate softening relationship. The path-dependent softening behaviour is solved in nonholonomic rate form within a quasiprescribed displacement formulation. At each event in the loading history, all equilibrium solutions for the prescribed mesh can be established and the critical equilibrium path with the minimum increment of external work adopted. The crack profile or trajectory is restricted in that it can only follow the interface boundaries of the defined mesh. No remeshing is carried out. Solutions to the nonholonomic rate formulation are obtained using a mathematical programming procedure based on the solution of an LCP. Several examples are given and compared, where possible, with published results. The advantage of this formulation is that branching and interacting cracks can be tracked subject to the limitations of the prescribed mesh.