This work presents an extended ordinary state-based peridynamics (XOSBPD) model for the non-spherical horizons. Based on the OSBPD, we derive the XOSBPD by introducing the Lagrange multipliers to guarantee the non-local dilatation and non-local strain energy density (SED) are equal to local dilatation and local SED, respectively. In this formulation, the XOSBPD removes the limitation of spherical horizons and is suitable for arbitrary horizon shapes. In addition, the presented XOSBPD does not need volume and surface correction and allows non-uniform discretization implementation with various horizon sizes. Three classic examples demonstrate the accuracy and capability for complex dynamical fracture analysis. The proposed method provides an efficient tool and in-depth insight into the failure mechanism of structure components and solid materials.

翻译：这项工作为非球界地平面提供了一种扩展的普通状态近光动力(XOSBPD)模型。根据OSBPD,我们通过引入拉格兰变异器来获取 XOSBPD,以保证非本地的扩展和非本地的菌株能量密度(SED)分别与本地的扩展和本地的SED相等。在这一配方中,XOSBPD消除了球界地平线的限制,适合任意的地平线形状。此外,提出的 XOSBPD不需要体积和表面的校正,允许以不同地平面大小实施非统一的离散化。三个典型例子显示了复杂动态断裂分析的准确性和能力。拟议方法提供了一个有效的工具,并深入地洞察结构组成部分和固体材料的故障机制。