An analytical singular element for the study of cohesive zone model based crack propagation

In the present study, a singular element is proposed to deal with crack propagation problem in which the nonlinear behavior in front of the crack tip is considered. And cohesive zone model (CZM) is used to simulate the nonlinear behavior. At first, a new singular element is constructed and further extended to deal with CZM based cracks. Cohesive tractions act on the cohesive crack surfaces can be approximately expressed in the form of polynomial. Then special solution corresponding to each expanding term is specified analytically so it has strictly satisfied the requirements of both differential equations of interior domain and the corresponding cohesive traction component acting on cohesive crack surface. Then the special solution can be transformed into nodal forces. Based on the situation of that the crack propagation is governed by cohesive laws an efficient iteration procedure is proposed. Finally, the cohesive crack propagation under arbitrary external loading can be simulated. In the present method the hypotheses of CZM are completely satisfied such that stress singularity vanishes and virtual crack length can be measured. And the validity of the present method is illustrated by numerical examples.