论文标题
一个新的无网状脆弱点方法（FPM）在每个点上具有最低未知数，用于在具有裂纹传播的两种理论下进行挠性分析。第二部分：验证和讨论
A New Meshless Fragile Points Method (FPM) With Minimum Unknowns at Each Point, For Flexoelectric Analysis Under Two Theories with Crack Propagation. Part II: Validation and discussion
论文作者
论文摘要
在这个两纸系列的第一部分中，提出了一种新的脆弱点方法（FPM），包括原始和混合配方，用于分析2D介电材料中的挠性效应。在本文中，提供了许多数值结果作为验证，包括线性和二次贴片测试，连续域中的挠性效应以及介电材料中固定裂纹的分析。还对电弹性应力的影响进行了讨论，这表明麦克斯韦的压力可能很重要，因此建议将完整的挠性理论用于纳米级结构。目前的原始和混合FPM还显示出它们在模拟裂纹启动和传播中具有柔韧性效应的适用性和有效性。柔韧性，加上压电效应，可以帮助，阻碍或偏转裂纹传播路径，在纳米级裂纹分析中不应忽略。在FPM中，在建模裂纹传播时，不需要重现或试验功能增强。新的键合能量速率（BER）基于基于压力的裂纹标准以及经典的基于应力的标准用于裂纹开发模拟。在我们的未来研究中将给出其他复杂的问题，例如动态裂纹的发展，断裂，碎片化和3D挠性分析。
In the first part of this two-paper series, a new Fragile Points Method (FPM), in both primal and mixed formulations, is presented for analyzing flexoelectric effects in 2D dielectric materials. In the present paper, a number of numerical results are provided as validations, including linear and quadratic patch tests, flexoelectric effects in continuous domains, and analyses of stationary cracks in dielectric materials. A discussion of the influence of the electroelastic stress is also given, showing that Maxwell stress could be significant and thus the full flexoelectric theory is recommended to be employed for nano-scale structures. The present primal as well as mixed FPMs also show their suitability and effectiveness in simulating crack initiation and propagation with flexoelectric effect. Flexoelectricity, coupled with piezoelectric effect, can help, hinder, or deflect the crack propagation paths and should not be neglected in nano-scale crack analysis. In FPM, no remeshing or trial function enhancement are required in modeling crack propagation. A new Bonding-Energy-Rate(BER)-based crack criterion as well as classic stress-based criterion are used for crack development simulations. Other complex problems such as dynamic crack developments, fracture, fragmentation and 3D flexoelectric analyses will be given in our future studies.
