This paper concerns developments in both classical and peridynamic (PD) finite deformation micropolar elasticity theory. The first part presents an alternative proof of a theorem that demonstrates variational consistency of the wryness measure in classical finite deformation micropolar elasticity which is one of the novel contributions of this work. The linearized version of the proposed wryness measure is compared with the wryness measure of small deformation micropolar elasticity. In the second part of this work, a finite deformation micropolar PD theory is presented. After proposing an additional integro-differential equation along with the standard PD equation of motion, the global balance of angular momentum is proved to be satisfied. The balance of virtual work is derived for the micropolar PD theory. Next, constitutive correspondence approach is used to relate PD force and moment states with their classical counterparts. The nonlocal versions of the strain and the proposed wryness measure are used in the constitutive correspondence. The constitutive equations of the classical micropolar theory are presented and how they can be incorporated in PD framework is discussed. We introduce a new bond breaking criterion for PD micropolar materials based on critical stretch and critical relative rotation. Quasi-static numerical simulations on deformations of plate with a hole and fracture of a double notched sheet are presented. Dynamic simulations concern wave propagation through a solid specimen and plate with a hole. Validation of the simulation results with the finite element solutions, boundary element solutions, and experimental observations demonstrate the potential of our approach.

中文翻译：

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有限变形微极近场动力学理论：wryness测度的变分一致性

本文关注经典和近场动力学 (PD) 有限变形微极弹性理论的发展。第一部分提出了定理的另一种证明，该定理证明了经典有限变形微极弹性中 wryness 测度的变分一致性，这是这项工作的新颖贡献之一。将所提出的 wryness 测量的线性化版本与小变形微极弹性的 wryness 测量进行比较。在这项工作的第二部分中，提出了有限变形微极局部放电理论。在提出附加的积分微分方程以及标准PD运动方程后，证明满足角动量的全局平衡。微极局部放电理论推导了虚功平衡。接下来，使用本构对应方法将局部放电力和力矩状态与其经典对应物联系起来。应变的非局部版本和建议的 wryness 度量用于本构对应。提出了经典微极性理论的本构方程，并讨论了如何将它们纳入 PD 框架。我们引入了基于临界拉伸和临界相对旋转的 PD 微极性材料的新键断裂准则。提出了带孔板变形和双缺口板断裂的准静态数值模拟。动态模拟涉及波通过固体样本和带孔板的传播。使用有限元解、边界元解和实验观察对模拟结果进行验证，证明了我们方法的潜力。