Peridynamics (PD) is a non-local continuum formulation. The original version of PD was restricted to bond-based interactions. Bond-based PD is geometrically exact and its kinematics are similar to classical continuum mechanics (CCM). However, it cannot capture the Poisson effect correctly. This shortcoming was addressed via state-based PD, but the kinematics are not accurately preserved. Continuum-kinematics-inspired peridynamics (CPD) provides a geometrically exact framework whose underlying kinematics coincide with that of CCM and captures the Poisson effect correctly. In CPD, one distinguishes between one-, two- and three-neighbour interactions. One-neighbour interactions are equivalent to the bond-based interactions of the original PD formalism. However, two- and three-neighbour interactions are fundamentally different from state-based interactions as the basic elements of continuum kinematics are preserved precisely. The objective of this contribution is to elaborate on computational aspects of CPD and present detailed derivations that are essential for its implementation. Key features of the resulting computational CPD are elucidated via a series of numerical examples. These include three-dimensional problems at large deformations. The proposed strategy is robust and the quadratic rate of convergence associated with the Newton--Raphson scheme is observed.

中文翻译：

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受连续运动学启发的近场动力学的计算框架

近场动力学 (PD) 是一种非局部连续体公式。PD 的原始版本仅限于基于债券的交互。基于键合的局部放电在几何上是精确的，其运动学类似于经典连续介质力学 (CCM)。但是，它无法正确捕捉泊松效应。这个缺点是通过基于状态的 PD 解决的，但运动学没有被准确地保留。受连续运动学启发的近场动力学 (CPD) 提供了一个几何精确的框架，其基本运动学与 CCM 的基本运动学一致，并正确捕捉泊松效应。在 CPD 中，可以区分一、二和三邻域的交互。邻域相互作用相当于原始 PD 形式的基于键的相互作用。然而，二邻域和三邻域相互作用与基于状态的相互作用有着根本的不同，因为连续运动学的基本元素被精确地保留下来。此贡献的目的是详细说明 CPD 的计算方面，并提供对其实施必不可少的详细推导。通过一系列数值示例阐明了所得计算 CPD 的关键特征。其中包括大变形下的三维问题。所提出的策略是稳健的，并且观察到与牛顿-拉夫森方案相关的二次收敛速度。通过一系列数值例子阐明了所得计算 CPD 的关键特征。其中包括大变形下的三维问题。所提出的策略是稳健的，并且观察到与牛顿-拉夫森方案相关的二次收敛速度。通过一系列数值例子阐明了所得计算 CPD 的关键特征。其中包括大变形下的三维问题。所提出的策略是稳健的，并且观察到与牛顿-拉夫森方案相关的二次收敛速度。