An extended bond-based peridynamic model with bond transverse deformation effects for quasi-brittle rocks

The bond-based peridynamics shows significant potential in describing and simulating the continuous-discontinuous problems like rock mass. However, the theory developed so far with account of the bond stretch and shear mechanisms exhibits unreasonable prediction of bond force and the appearance of negative shear stiffness when Poisson’s ratio exceeds a critical value. In this work, the root cause behind the negative shear stiffness problems is identified and solved by originally incorporating the effect of transverse deformation in addition to the bond stretch and rotation. In this way, the elastic response of peridynamic bond is completed and becomes multi-dimensional. Also, the bond-scale formulations can be regarded as a nonlocal version of the generalized Hooke’s Law. A novel multi-dimensional bond-based peridynamic model is developed, which is capable of describing rock deformation and mixed-mode fracture process. Several benchmark tests are performed to assess the effectiveness and robustness of the method. The proposed model not only overcomes the theoretical deficiency of traditional ones but also allows more suitable description and simulation of rock behavior on different scales.