A simple J-integral governed bilinear constitutive relation for simulating fracture propagation in quasi-brittle material

The present paper develops a bilinear constitutive relation for material at fracture tip based on the cohesive zone model and the J-integral theory. In this bilinear constitutive relation, the stress linearly decreases rather than suddenly drops down to zero at the post-peak stage. The slope of stress degradation is related to the critical J-integral of material and the element size. By this bilinear constitutive relation, the tensile and mixed fracture propagation can be well simulated for the strain energy release rate can be preserved with element size decreasing. The simulation results are almost free of the element size sensitivity. The present model and its implementation are very simple. For the elements at fracture tip, the derived bilinear constitutive relation is adopted while for the rest elements, the ideal elastic-brittle model is adopted. For the fracture propagation is represented by the deterioration of stiffness through constitutive relation, no separate fracture criterion is needed, which makes the evaluation of the fracture propagation by separate fracture criterion and the mesh modification after each load step unnecessary. The simulation examples of tensile and mixed fracture suggest that the present method is valid and highly efficient.