Numerical simulation of crack propagation with equivalent cohesive zone method based on virtual internal bond theory

The virtual multi-dimensional internal bond (VMIB) model is developed within the framework of the virtual internal bond (VIB) theory. The VIB theory considers a solid as a three-dimensional network consisting of randomized material particles at the microscopic scale, which are bonded with VIBs possessing “normal stiffness”. In VMIB, however, the material particles are bonded with virtual normal bonds possessing both normal stiffness and shear stiffness. The macroscopic constitutive relationship is derived in terms of the normal and shear stiffness of the bonds. In this paper, we use the VMIB to simulate propagation of the pre-existing cracks with the equivalent cohesive zone (ECZ) method. To make the cracked body a seamless continuum, an ECZ is embedded into the pre-existing crack. The ECZ has the same microstructure as the surrounding material, but an initial internal deformation is assigned to it to ensure that the interaction between the two crack faces is negligible. Thereafter, the ECZ can behave as a pre-existing crack. For the ECZ possesses the same microstructure with the surrounding material, the ‘mended’ cracked body can be described with a uniform constitutive relation. The properties of the pre-existing cracks are implicitly incorporated into the constitutive relationship of VMIB. The advantages of this method are that: (i) the meshing process can be carried out regardless of the geometrical integrity of cracked material; (ii) remeshing is not necessary when crack propagates and (iii) the fracture criterion is embedded into the constitutive relationship. The example simulation shows that the method is efficient and feasible.