围压应力是静态的第一Piola-Kirchhoff维里应力
Peridynamic stress is the static first Piola-Kirchhoff Virial stress
摘要：
Lehoucq和Silling [1，2]提出的围压应力公式在数值计算中实施起来比较麻烦。本文通过Hardy-Murdoch方法[5，6]证明了围压应力张量与源于Irving-Kirkwood-Noll形式[3，4]的第一个Piola-Kirchhoff静态维里应力张量具有精确的数学表达式，从而为围压应力的数值计算提供了一个简单明了的表达式。通过数值计算，验证了所提出的周向应力公式在预测裂纹尖端及其它应力集中源附近应力状态方面的准确性。在基于粘结的周向应力模型中，采用原型微弹性脆性（PMB）材料模型计算周向应力。结果表明，PMB材料模型在大变形下可能表现出非线性本构行为。计算结果与有限元分析结果、解析解和实验数据吻合较好，表明所提出的周向应力公式在模拟含不连续性问题的应力状态方面具有良好的潜力，特别是在基于键合的周向应力问题中。
英文摘要：
The peridynamic stress formula proposed by Lehoucq and Silling [1, 2] is cumbersome to be implemented in numerical computations. Here, we show that the peridynamic stress tensor has the exact mathematical expression as that of the first Piola-Kirchhoff static Virial stress originated from Irving-Kirkwood-Noll formalism [3, 4] through the Hardy-Murdoch procedure [5, 6], which offers a simple and clear expression for numerical calculations of peridynamic stress. Several numerical verifications have been carried out to validate the accuracy of proposed peridynamic stress formula in predicting the stress states in the vicinity of the crack tip and other sources of stress concentration. The peridynamic stress is evaluated within the bond-based peridynamics with prototype microelastic brittle (PMB) material model. It is found that the PMB material model may exhibit nonlinear constitutive behaviors at large deformations. The stress fields calculated through the proposed peridynamic stress formula show good agreements with finite element analysis results, analytical solutions, and experimental data, demonstrating the promising potential of derived peridynamic stress formula in simulating the stress states of problems with discontinuities, especially in the bond-based peridynamics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
