扩展键基近场动力学的几何非线性扩展

Geometrical Nonlinear Extension of Extended Bond-Based Peridynamic Model

摘要:

扩展键基近场动力学模型解决了经典模型中固定泊松比的限制问题，但是仅限应用于小变形情况下的模拟。提出了一种计算键变形的实现方法，利用有限变形理论中的描述使模型能够处理几何非线性问题。 通过最小二乘拟合得到物质点的局部位移场，再对位移函数求导得到局部域的变形梯度张量。固体的旋转与拉伸通过对变形梯度张量的极分解分离，从而将扩展键的变形部分从总体位移中提取。随后，通过对变形系统的各个键力进行积分，从而获得系统大变形的正确预测结果。最后，开展了几个基准测试，与非线性有限元结果进行对比并验证了所提出模型的有效性和精确性。

关键词:扩展键基近场动力学模型;大变形;几何非线性;极分解

Abstract:

The extended bond-based peridynamic （XPD） model resolved the limitation of fixed Poisson’s ratio in the classical model for small deformation problems. In this paper， a novel implementation using the finite deformation formulation is proposed to deal with geometrical nonlinear problems. The rotation of solid is calculated by the polar decomposition of the deformation gradient tensor derived from the least square fitting of the local displacement field. Therefore， the deformed part of the bond deflection can be separated from the general displacements， and then correct large deformation predictions can be obtained by integrating each bond force of the deformed system. Several benchmark studies are presented to demonstrate the predictive ability of the proposed model.

Key words:extended bond-based peridynamic (XPD) model;large deformation;geometrical nonlinearity;polar decomposition