离散键基周向介质各向异性的通用数值模拟方法
A General Numerical Method to Model Anisotropy in Discretized Bond-Based Peridynamics
摘要：
本文提出了一种新的、通用的、鲁棒的方法来确定各向异性线弹性键基周波材料的键微模量。找到一个离散分布的键的微模量，再现各向异性的周向刚度张量的问题被铸造作为一个最小二乘问题。所提出的数值方法是能够找到一个分布的键微模量，能够准确地再现所需的各向异性刚度张量提供的条件满足柯西关系。所有八种可能的弹性材料对称性的例子，从三斜各向同性给出并深入讨论。参数研究表明，数值方法是足够强大的处理各种水平尺寸，邻域形状，影响函数和晶格旋转效应。最后，一个例子的问题，以证明所提出的方法是物理上的声音，并同意从经典弹性力学的解析解的解决方案。所提出的方法具有很大的潜力，在各向异性材料的变形和断裂与键基周向力学建模。
英文摘要：
This work proposes a novel, general and robust method of determining bond micromoduli for anisotropic linear elastic bond-based peridynamics. The problem of finding a discrete distribution of bond micromoduli that reproduces an anisotropic peridynamic stiffness tensor is cast as a least-squares problem. The proposed numerical method is able to find a distribution of bond micromoduli that is able to exactly reproduce a desired anisotropic stiffness tensor provided conditions of Cauchy's relations are met. Examples of all eight possible elastic material symmetries, from triclinic to isotropic are given and discussed in depth. Parametric studies are conducted to demonstrate that the numerical method is robust enough to handle a variety of horizon sizes, neighborhood shapes, influence functions and lattice rotation effects. Finally, an example problem is presented to demonstrate that the proposed method is physically sound and that the solution agrees with the analytical solution from classical elasticity. The proposed method has great potential for modeling of deformation and fracture in anisotropic materials with bond-based peridynamics.
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