论文标题
有效的基于图的拉伸强度模拟随机纤维结构
Efficient Graph-based Tensile Strength Simulations of Random Fiber Structures
论文作者
论文摘要
在本文中，我们提出了一个模型模拟框架，用于随机纤维结构的虚拟拉伸强度测试，因为它们出现在非织造材料中。重点是相对于问题关系的多尺度和随机性的有效处理。特别是，宏观规模上随机微观结构和确定性结构生产相关的特征的相互作用使基于经典均匀化的方法计算复杂且昂贵。在我们的方法中，我们将配备非线性弹性材料定律的纤维结构建模为基于图和桁架类型的纤维结构。通过一系列力平衡来描述拉伸强度测试，相对于各种边界条件，它将其嵌入到奇异的扰动动力系统中是有利的，就有关解决方案理论和数值方法的收敛性而言，它是有利的。问题缩写的数据减少提供了额外的加速，蒙特卡洛模拟说明了随机性。这项工作是概念的证明，并为优化开放了该领域。
In this paper, we propose a model-simulation framework for virtual tensile strength tests of random fiber structures, as they appear in nonwoven materials. The focus is on the efficient handling with respect to the problem-inherent multi-scales and randomness. In particular, the interplay of the random microstructure and deterministic structural production-related features on the macro-scale makes classical homogenization-based approaches computationally complex and costly. In our approach we model the fiber structure to be graph-based and of truss-type, equipped with a nonlinear elastic material law. Describing the tensile strength test by a sequence of force equilibria with respect to varied boundary conditions, its embedding into a singularly perturbed dynamical system is advantageous with regard to statements about solution theory and convergence of numerical methods. A problem-tailored data reduction provides additional speed-up, Monte-Carlo simulations account for the randomness. This work serves as a proof of concept and opens the field to optimization.
