In this paper, we propose a model-simulation framework for virtual tensile strength testing of random fiber structures, such as those in nonwoven materials. The focus is on efficient handling of the problem-inherent multi-scales and randomness. In particular, the interplay between 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 as graph-based and of truss-type, equipped with a nonlinear elastic material law. The tensile strength test is described by a sequence of force equilibria with varied boundary conditions. Its embedding into a singularly perturbed dynamical system is advantageous with respect to statements on solution theory and convergence of numerical methods. A problem-tailored data reduction provides additional speed-up, while Monte-Carlo simulations account for randomness. This work serves as a proof of concept and opens the field for optimization.

中文翻译：

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随机纤维结构的基于图形的高效拉伸强度模拟

在本文中，我们提出了一种用于随机纤维结构（例如非织造材料中的结构）的虚拟拉伸强度测试的模型模拟框架。重点是有效处理问题固有的多尺度和随机性。特别是，宏观尺度上随机微观结构和确定性结构生产相关特征之间的相互作用使得基于均质化的经典方法计算复杂且成本高昂。在我们的方法中，我们将纤维结构建模为基于图形的桁架类型，并配备非线性弹性材料定律。拉伸强度测试由一系列具有不同边界条件的力平衡来描述。它嵌入到奇异摄动动力系统中，对于求解理论和数值方法的收敛性的陈述是有利的。针对问题的数据简化提供了额外的加速，而蒙特卡洛模拟考虑了随机性。这项工作作为概念证明并打开了优化领域。