Numerical simulation for fracture propagation of multi-cracked rock materials using virtual multidimensional internal bonds

Virtual multidimensional internal bonds(VMIB) was a multiscale mechanical model based on the Virtual Internal bond(VIB) theory.From the view of VIB and VMIB,the microstructures of intact materials and cracked materials were consistent in that both the two materials consisted of network constructed by the randomized materials particles and virtual internal bonds in micro scale.For the cracked materials,the distance of material particles at the pre-existing crack was so large that the interaction(bond stiffness) between particles becomes negligible in micro scale,leading to the macro crack.To simulate the pre-existing crack,an initial deformation was assigned to the aggregate of material particles at the pre-existing crack.The assigned initial deformation was large enough to make interaction between material particles negligible,so as to represent the behavior of the pre-existing crack.By use of this method,the effect of the pre-existing crack was incorporated into the constitutive relation of materials,hence,the cracked materials could be described by the uniform constitutive relationship,which made the present method free of the special treatment of cracks on the element discretization level as the conventional continuum mechanics method did.Moreover,the VMIB was discrete at the constitutive level and the failure criterion had been embedded into the constitutive relation by the bond evolution function,so it was free of the problem of remeshing and choice of external fracture criterion when the failure process was simulated.By simulating the fracture process of a square plate containing two parallel pre-existing cracks,the present method is indicated to be capable of representing the fracture propagation and the failure process of multi-cracked rock materials.