Multiscale shear fracture of heterogeneous material using the virtual internal bond

Material behavior entails multiscaling. The macro response of materials is affected by the microstructure. The method of VMIB (virtual multidimensional internal bond) developed from the VIB (virtual internal bond) for the continuum consists of discrete microscopic mass particles. These mass particles are connected with virtual bond possessing both normal and shear stiffness. The macro constitutive relation is derived in terms of bond stiffness. Shear fracture simulation of heterogeneous material involves introducing heterogeneity into the constitutive relation by two ways. First, heterogeneous material may consist of micro components with different stiffness. This character represented by the bond stiffness is assumed to be randomly distributed. Second, the micro components composed of the heterogeneity may possess the same stiffness, but their critical deformation, say the strain strength, may be different. This character represented by the strain strength is assumed to be randomly distributed. For a given statistical distribution function, the bond stiffness and the strain strength can be generated in numerical simulation implementation. Using VMIB, the macro response of materials is determined by the evolution of bond at the microscopic scale. To reflect micro mechanism of shear fracture, a phenomenological bond evolution function is proposed such that the shear fracture process of heterogeneous material is simulated. The results demonstrate that the present method can represent the shear fracture process and the basic characteristics of shear fracture of heterogeneous material.