This article introduces the R² Fill method, which is an algorithm for filling a region with particles isotropically. The method's isotropy is tested geometrically and then mechanically with the Discrete Element Method (DEM). It applies to planar and three-dimensional problems and is simpler to implement and has competitive metrics compared to other Advancing Front packing algorithms. The DEM formulation used in this paper provides a way to model solid materials and eliminate residual stress created in any particle packing algorithm. The R² Fill method was tested over ranges of particle sizes. At large size ranges the method generated a higher coordinate number and denser particle packing, with 79.718% fill at the maximum tested size range. The geometric isotropy was improved at higher size ranges yielding less than a 1% isotropic error. The method also had fewer particles than the similar and more complex algorithm by Yongjun Li. Lastly we tested mechanical isotropy by using our DEM formulation to measure the stress–strain response under a tensile load at different orientations. The R² Fill method produced mechanical isotropy within 2% error for the elastic moduli, shear moduli, and Poisson ratio.

中文翻译：

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粒子模拟的各向同性堆积算法

本文介绍了R ² Fill 方法，该方法是一种用粒子各向同性填充区域的算法。该方法的各向同性先进行几何测试，然后使用离散元方法 (DEM) 进行机械测试。它适用于平面和三维问题，与其他 Advancing Front 打包算法相比，它更易于实现且具有竞争性指标。本文中使用的 DEM 公式提供了一种模拟固体材料和消除任何粒子堆积算法中产生的残余应力的方法。的- [R ²填充方法在粒径范围内进行了测试。在大尺寸范围内，该方法产生了更高的坐标数和更密集的颗粒堆积，在最大测试尺寸范围内填充率为 79.718%。几何各向同性在更高的尺寸范围内得到改善，各向同性误差小于 1%。与李永军的类似且更复杂的算法相比，该方法的粒子更少。最后，我们使用我们的 DEM 公式测试了机械各向同性，以测量不同方向拉伸载荷下的应力 - 应变响应。的- [R ²填充方法制造2％的误差内的机械各向同性的弹性模量，剪切模量和泊松比。