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.

中文翻译：

---

基于离散键的近场动力学模拟各向异性的新数值方法

这项工作提出了一种新颖、通用和稳健的方法，用于确定基于各向异性线性弹性键的近场动力学的键微模量。寻找重现各向异性近场动力学刚度张量的键微模量的离散分布的问题被视为最小二乘问题。如果满足柯西关系的条件，所提出的数值方法能够找到能够精确再现所需各向异性刚度张量的键微模量分布。给出并深入讨论了从三斜到各向同性的所有八种可能的弹性材料对称性的示例。进行参数研究以证明该数值方法足够稳健，可以处理各种视界大小、邻域形状、影响函数和晶格旋转效应。最后，提出了一个示例问题，以证明所提出的方法在物理上是合理的，并且该解与经典弹性的解析解一致。所提出的方法在基于键的近场动力学模拟各向异性材料的变形和断裂方面具有巨大潜力。