A new quasi-continuum constitutive model for crack growth in an isotropic solid

A new quasi-continuum constitutive model is established based on the randomized cohesive bonds model proposed by Gao and Klein (1998). This model bridges the microscopic discrete constitution characters and the macroscopic mechanical properties of material. In the presented constitutive model, both the bond stretch energy potential and the rotation energy potential are considered, which makes the presented constitutive model applicable to different Poisson-ratio and Young's modulus materials. By establishing a phenomenological bond stiffness function according to the complete stress–strain relationship of uniaxial tension test, the fracture criterion is directly incorporated into the constitutive model. The method requires no external fracture criterion when simulating fracture initiation and propagation, which brings convenience in the numerical simulation. At last, the presented constitutive model is applied to an example of crack growth in an isotropic solid.