Displacement discontinuity method for cohesive crack propagation

Displacement discontinuity method (DDM) can conveniently solve fracture mechanics problems because the discontinuous displacement field across the fracture surfaces can be explicitly captured by the displacement discontinuity elements. However, the potential of DDM on solving crack propagation problems in quasi-brittle materials has not been covered in the past. In this paper, the DDM is extended to take into account the fracture process zone in quasi-brittle materials such as concrete by incorporating an iterative algorithm to account for the cohesive stress vs crack opening relation. Tensile strength criterion and fracture toughness criterion for crack propagation are used respectively for two corresponding types of crack tip element-parabolic displacement discontinuity element (PDDE) and root-r displacement discontinuity element (RRE). Numerical simulations of the wedge splitting test and three-point bending of notched beam are performed. The results are found to compare well with experimental and finite element results simulations.