论文标题
一种在基于离散键的Peridyanics中对各向异性建模的一般数值方法
A General Numerical Method to Model Anisotropy in Discretized Bond-Based Peridynamics
论文作者
论文摘要
这项工作提出了一种新型，一般和健壮的方法，用于确定各向异性线性弹性键基的蛋白动力学的键微杜地。发现键合的键微型杜比的离散分布的问题是将各向异性的动力刚度张量作为最小二乘问题。所提出的数值方法能够找到键合微杜地的分布，该分布能够准确地重现所需的各向异性刚度张量，只要满足考子关系的条件。给出并深入讨论所有八种可能的弹性物质对称性的示例，从三斜向到各向同性。进行了参数研究以证明数值方法足以处理各种范围，邻域形状，影响功能和晶格旋转效应。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正确的，并且该解决方案与经典弹性的分析解决方案一致。所提出的方法具有具有基于键基的植入动力学的各向异性材料中变形和断裂建模的潜力。
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.
