Abstract Javili et al. recently reported a continuum-kinematics-inspired peridynamic model, in which theoretical aspects regarding the balance of linear and angular momentum and other conservation principles are considered. However, the analytical formulation of the model constants and the microelastic potential energy functions and numerical implementation were not defined. In this paper, a novel linear elastic constitutive model is proposed for the continuum-kinematics-inspired peridynamics by introducing specific expressions for various interaction potentials. The one-neighbor interaction potential equivalent to conventional bond-based interaction potential is utilized to account for the constitutive relationship within line elements between two material points. In contrast, the two- and three-neighbor interaction potentials are employed to consider the areal and volumetric effects under general mechanical loads. Three relevant material parameters are introduced and derived from energy equivalence to a classical linear elastic continuum mechanics model. Equipped with the three types of interaction potentials, the novel continuum-kinematics-inspired peridynamics is extended from classical bond-based peridynamics, wherein the two interaction force vectors within a bond are unequal and not parallel to the bond direction, can be regarded as an alternative version of non-ordinary state-based peridynamics. The proposed model is numerically demonstrated to be effective in absolutely eliminating the restriction of the fixed Poisson’s ratio in classical bond-based peridynamics, notably improving the effectiveness of the other enriched bond-based peridynamics in reproducing the elastic deformation of solids subjected to heterogeneous deformation fields and completely removing the numerical oscillations in non-ordinary state-based peridynamics.

中文翻译：

---

一种受连续运动学启发的近场动力学的新型线弹性本构模型

摘要 Javili 等人。最近报道了一种受连续运动学启发的近场动力学模型，其中考虑了有关线性和角动量平衡以及其他守恒原理的理论方面。然而，模型常数和微弹性势能函数的解析公式和数值实现没有定义。在本文中，通过引入各种相互作用势的特定表达式，为连续体运动学启发的近场动力学提出了一种新的线弹性本构模型。等效于传统的基于键的相互作用势的单邻相互作用势用于解释两个材料点之间线元素内的本构关系。相比之下，两个和三个邻域相互作用势用于考虑一般机械载荷下的面积和体积效应。引入了三个相关的材料参数，并从经典线弹性连续介质力学模型的能量等价导出。配备了三种相互作用势，新的连续体运动学启发的近场动力学是从经典的基于键的近场动力学扩展而来的，其中键内的两个相互作用力矢量不相等且不平行于键方向，可以看作是一个非普通的基于状态的近场动力学的替代版本。所提出的模型被数值证明可以有效地完全消除基于键的经典近场动力学中固定泊松比的限制，