We begin the article by summarizing some key developments in the field of Peridynamics (PD) and arrive at a conclusion that two schools of PD are emerging in recent years. One school takes a more traditional view of PD as a model of a nonlocal continuum, while another approaches PD as a discretization methodology for local continua where the nonlocality is reduced under mesh refinement. Adhering to the latter viewpoint, we develop a PD formulation using the now classical, yet continuously evolving Microplane constitutive model (M7) developed for the failure analysis of concrete materials. We show how to incorporate the M7 model into correspondence-based PD (also known as the non-ordinary state-based PD) and validate the formulation using an extensive set of classical fracture tests. We also propose an extension of the M7 model to handle concrete fracture and fragmentation in the PD context.

我们通过总结近场动力学 (PD) 领域的一些关键发展来开始本文，并得出一个结论，即近年来出现了两个 PD 学派。一所学校将PD 视为非局部连续体的模型，而另一所学校则将PD 视为离散化在网格细化下减少非局部性的局部连续体的方法。秉承后一种观点，我们使用现在经典但不断发展的微平面本构模型 (M7) 开发了一种 PD 公式，该模型是为混凝土材料的失效分析而开发的。我们展示了如何将 M7 模型合并到基于对应的 PD（也称为基于非普通状态的 PD）中，并使用一组广泛的经典断裂测试来验证该公式。我们还提出了 M7 模型的扩展，以处理 PD 上下文中的混凝土断裂和破碎。