Peridynamics is based on integro-differential equations and has a length scale parameter called horizon which gives peridynamics a non-local character. Currently, there are three main peridynamic formulations available in the literature including bond-based peridynamics, ordinary state-based peridynamics and non-ordinary state-based peridynamics. In this study, the optimum horizon size is determined for ordinary state-based peridynamics and non-ordinary state-based peridynamics formulations by using uniform and non-uniform discretisation under dynamic and static conditions. It is shown that the horizon sizes selected as optimum sizes for uniform discretisation can also be used for non-uniform discretisation without introducing significant error to the system. Moreover, a smaller horizon size can be selected for non-ordinary state-based formulation which can yield significant computational advantage. It is also shown that same horizon size can be used for both static and dynamic problems.

Peridynamics基于整数微分方程，并且具有一个称为“ Horizo​​n”的长度比例参数，该参数使Peridynamics具有非局部特性。当前，文献中提供了三种主要的围动力公式，包括基于键的围动力，基于普通状态的围动力和基于非状态状态的围动力。在这项研究中，通过在动态和静态条件下使用均匀和非均匀离散化，确定基于普通状态和非普通状态的周围动力学公式的最佳视界大小。结果表明，选择的水平尺寸作为均匀离散化的最佳尺寸，也可以用于非均匀离散化，而不会给系统带来明显的误差。此外，对于基于非常规状态的公式，可以选择较小的视野范围，这可以产生显着的计算优势。还显示出相同的视域大小可用于静态和动态问题。