A Non-Ordinary State-Based Peridynamics Elastic-Plastic Model Based on Hoek-Brown Criterion

Abstract:

The rock medium has obvious elastic-plastic deformation characteristics and fracture mechanics behavior at different loads. In order to simultaneously describe the continuous field of elastic-plastic deformation and the discontinuous field of fracture mechanics behavior of rock， a non-ordinary state-based peridynamics （NOSBPD） elastic-plastic model based on the Hoek-Brown strength criterion is proposed in this paper. First， based on the material correspondence in the non-local deformation framework， the NOSBPD elastic-plastic constitutive equation with the Hoek-Brown strength criterion is established. The stress increment corresponding to a given strain increment is obtained through the return mapping algorithm of the principal stress space， and the corresponding incremental model integration algorithm is given. Then， a fracture criterion based on equivalent plastic strain is proposed， which can realize the characterization of the mechanics behavior of the whole process of rock elastic-plastic fracture. Finally， the zero-energy mode problem of NOSBPD simulation is eliminated by introducing a non-uniform deformation state. Based on the comparison and analysis of the numerical simulation results in this paper with the finite element method and experimental data， the correctness of the model proposed is verified. This paper provides an effective analysis method for the study of elastic-plastic fracture mechanics behavior of rock.