An extended quasi-bond method with isoparametric implementation for fracture problems in rock-like materials

Efficient and accurate prediction of damage and fracture remains one of main challenges in solid mechanics and computational mechanics. While the original quasi-bond method (QBM) has demonstrated its applicability in simulating solid deformation and characterizing crack nucleation and propagation, it remains the issue of fixed Poisson’s ratio and its numerical implementation still relies on computationally intensive calculation of geometric intersection points between quasi-bonds and element edges (sides) and lacks a standardized method for assembling the system’s stiffness matrix. In this paper, the effects of shear deformation are first incorporated into the QBM theory in order to remove the limitation of Poisson’s ratio. An isoparametric quasi-bond method is developed by introducing an integral transformation technique, which establishes a unified approach of constructing a system of quasi-bonds for both 2D and 3D problems. When comparing with the conventional operation, the present technique allows reducing computational cost of the initialization process while achieving higher numerical accuracy with a lower bond density. The proposed QBM exhibits lower matrix bandwidth compared to peridynamics approach, and eliminates the need for calculating continuous damage field as required in phase-field method, thereby combining computational efficiency with simplicity. Furthermore, the isoparametric formulation leads to an efficient and natural QB–FE coupling, which provides a seamless interface for integration into commercial finite element programs. Various validations through typical benchmark tests confirm computational efficiency of the proposed approach in solving both elasticity and elastic fracture problems.