Multiscale simulation of fracture propagation in heterogeneous materials using virtual multidimensional internal bonds

作者：Zhang Z N^*

来源：Theoretical and Applied Fracture Mechanics, 2008, 49(3): 233-241.

DOI：10.1016/j.tafmec.2008.02.001

• crack propagation
• numerical simulation
• heterogeneity
• virtual multidimensional internal bonds
• brittle material
• rock

The virtual multidimensional internal bonds (VMIB) model is developed based on the virtual internal bond (VIB) theory. In VMIB, a shear effect is introduced into the interactions of material particles in microscale, which makes VMIB capable of representing different Poisson ratios. The presented paper firstly develops a technique to model the pre-existing cracks distributed in heterogeneous materials. Viewed from the macro scale, the cracked material is discontinuous. The discontinuity brings difficulties to the mechanical description in continuum mechanics. However, if viewed from the micro scale, the cracked material retains the same micro structure constructed with virtual bond and material particles as the intact material. The difference between the intact and cracked material is that the distance of micro material particles at crack is so far that the bond stiffness is negligible for cracked material. The cracked material can be described with a uniform constitutive model since the VMIB constitutive relationship is founded on the microstructure. To represent the effect of crack, the microelement intersected by crack is assigned an initial deformation large enough to make the micro bond stiffness negligible. By this method, the crack effect is incorporated into the constitutive relationship. To represent the heterogeneity of the matrix material, the bond stiffness is assumed to statistically distribute. The fracture criterion is incorporated into the constitutive relationship via bond evolution function. The macro fracture propagation pattern is determined by the rupture mechanism of micro bond. If the bond rupture is dominated by the bond rotation deformation, the macro fracture propagation mode displays a shear one while a tensile one if bond rupture is dominated by the bond stretch deformation. If both bond deformations contribute to the rupture, the macro propagation mode displays a mixed one. The simulation results indicate that the presented method is capable of simulating the crack propagation process in heterogeneous materials. The merits of the presented method are that (i) the meshing procedures can be carried out regardless of the geometry integrity of cracked materials; (ii) it does not need to modify the mesh scheme when crack initiates and propagates; (iii) no external fracture criterion is needed since the failure criterion has been embedded into the constitutive relationship via bond evolution function. However, the drawback of the method is that the interested domain should be finely meshed to ensure the simulation accuracy.

• 出版日期2008-6
• 单位上海大学