Simulation of fracture propagation subjected to compressive and shear stress field using virtual multidimensional internal bonds

Abstract The virtual multidimensional internal bonds (VMIB) model and its predecessor, the virtual internal bond (VIB) model, belong to a special class of continuum mechanics methods that are aimed to simulate fractures with no additional fracture criterion apart from the constitutive laws of the material. However, in the simulation of the fracture subjected to compressive and shear stress field, the contact and friction effect of fracture faces is significant. To resolve this problem, the present paper, taking advantage of the geometrical characteristics of the three-node triangular element (TTE), develops a three-node contact element (TCE) based on the finite element method. A TCE consists of two contact pairs, through which the stiffness matrix of TCE is derived. The pre-existing fracture is represented by transforming the TTE intersected by fracture into the TCE, which allows the meshing procedure to proceed regardless of the pre-existing fractures. During the simulation process, the failure of an intact TTE yields a ‘micro’ fracture at the element level. These ‘micro’ fractures align to form a ‘macro’ fracture. To represent the newly generated fracture, the TTEs identified to fail are automatically transformed into the TCEs. As the TCE shares the common nodes with the intact TTE, the transformation from TTE to TCE is accomplished without any modification on the original mesh format, which makes the fracture simulation highly efficient and simple. The simulation examples indicate that the present method can efficiently simulate the fracture propagation subjected to shear and compressive stress.