The plastic behaviors of geomaterials often obey non-associated flow rule. In this paper, a two-dimensional (2D) ordinary state-based peridynamic (OSB-PD) increment model with shear deformation based on Drucker-Prager (D-P) criterion with non-associated flow rule is proposed to study the plastic behavior of geomaterials. An incremental form of peridynamic (PD) strain energy density for plane elastic problems is first established. The material parameters are determined when the incremental PD strain energy density is equal to the incremental strain energy density in classical mechanics. The PD force density for the OSB-PD theory with shear deformation in plane elastic cases is derived accordingly. The relationship between the incremental second invariant of the stress tensor $d{J}_2$, the first invariant function of stress tensor $d{I}_1$ in the classical mechanics and PD are established in this paper, and the Drucker-Prager yield surface is expressed in the framework of peridynamics. To avoid the excessive plastic dilation, the non-associated flow rule is proposed, in which isotropic and deviatoric plastic elongation are employed to describe the plastic behaviors of a bond. Also, the equivalent stress and equivalent plastic strain for the proposed PD model are given. An integration algorithm for the proposed increment model is developed. Numerical examples including circular opening in rocks are performed, and the PD results are compared with that obtained by the finite element method or analytical solution. Those numerical simulations have verified the validity of the proposed PD model to predict the elasto-plastic behavior of geomaterials.

岩土材料的塑性行为往往服从非关联流动规则。在本文中，基于非关联流动规则的 Drucker-Prager (DP) 准则，提出了具有剪切变形的二维 (2D) 基于普通状态的近场动力学 (OSB-PD) 增量模型来研究岩土材料的塑性行为。 . 首先建立了平面弹性问题的近场动力学 (PD)应变能密度的增量形式。当增量 PD 应变能密度等于经典力学中的增量应变能密度时，确定材料参数。相应地推导出具有平面弹性情况下剪切变形的 OSB-PD 理论的 PD 力密度。应力张量增量第二不变量之间的关系$d{J}_2$, 应力张量的第一不变函数 $d{\mathrm{一世}}_1$本文建立了经典力学中的 PD 和 PD，并在近场动力学的框架内表达了 Drucker-Prager 屈服面。为了避免过度的塑性膨胀，提出了非关联流动规则，其中使用各向同性和偏塑性伸长率来描述键的塑性行为。此外，还给出了所提出的 PD 模型的等效应力和等效塑性应变。一个积分算法为建议的增量模型开发。进行了包括岩石圆形开口在内的数值算例，并将PD结果与有限元法或解析解得到的结果进行了比较。这些数值模拟验证了所提出的 PD 模型在预测土工材料弹塑性行为方面的有效性。