基于Hoek-Brown准则的非常规态型近场动力学弹塑性模型

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

摘要:

岩石介质在不同荷载环境下具有显著的弹塑性变形特征和断裂力学行为。为了同时描述岩石的弹塑性变形连续场以及断裂力学行为的非连续场，提出了一种基于Hoek-Brown强度准则的非常规态型近场动力学（non-ordinary state-based peridynamics， NOSBPD）弹塑性模型。首先，基于非局部变形框架下的材料对应性关系，建立了以Hoek-Brown强度准则为屈服准则的NOSBPD弹塑性本构方程，通过主应力空间的返回映射算法得到给定应变增量对应的应力增量，并给出了相应的增量模型积分算法；其次，提出了基于等效塑性应变的断裂准则，实现了岩石弹塑性断裂全过程力学行为的表征；最后，通过引入非均匀变形状态消除了NOSBPD模拟存在的零能模式问题。基于数值模拟结果与有限元结果以及试验数据进行对比分析，验证了所建立模型的正确性，可为岩石的弹塑性断裂力学行为研究提供有效分析手段。

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.