Multiscale modeling of the anisotropic elastic-plastic behavior of paper

纸张在许多与技术相关的应用中越来越重要，特别是在包装行业，因为它是一种可再生的原材料，很容易回收利用。尽管纸已经使用了大约2000年，但人们对纸的材料行为及其模型仍然没有足够的了解。纸张材料建模的挑战在于它的多尺度特性。由纤维网络组成的本征微观结构对材料的宏观响应有很大的影响。为了应对这一挑战，本项目将制定一种数值模拟策略。这一战略的目的是在结构尺度上有效地描述材料，同时考虑网络尺度的影响。因此，可以隔离和研究单个参数和效应对宏观行为的影响，这在实验装置中是几乎不可能的。工作计划被分成几个工作包。首先，为光纤网络生成代表性体积元素(RVE)。通过这些，可以分析由于诸如纤维长度和单个纤维的材料特性等几何数据的统计分布而导致的宏观尺度上的表观特性的变化。然后，基于有限元方法，将这些RVE实现到Fe2框架中。为了以合理的计算代价高效地进行相应的模拟，采用适当的正交分解技术对模型进行降维。本项目的结果是一个仿真工具，能够高效、稳健地描述纸张的材料行为，同时考虑到微尺度效应。此外，对光纤和网络水平上的不同影响如何相互作用产生了更深层次的理解，这是纯粹的实验研究不可能做到的。

Paper is gaining more and more importance in numerous technically relevant applications, in particular in the packaging industry, because it is a renewable raw material and easily recyclable. Even though paper has been in use for around 2000 years, the material behavior and its modeling are still not sufficiently understood. The challenge in the material modeling of paper is its multiscale nature. The intrinsic microstructure, which consists of a fiber network, has a significant effect on the macroscale material response. To tackle this challenge, a numerical modeling strategy is to be developed in the current project. This strategy aims at an efficient description of the material on the structural scale while simultaneously accounting for the effects of the network scale. Thereby, the influence of single parameters and effects on the macroscopic behavior can be isolated and investigated, which is hardly possible with an experimental setup.The work plan is divided into several work packages. First, representative volume elements (RVE) are generated for the fiber networks. With these, the variation of apparent properties on the macroscale due to statistical distributions of geometrical data such as fiber length and material properties of single fibers can be analyzed. Then, these RVE are implemented into the FE2 framework based on the finite element method. In order to perform the corresponding simulations efficiently with reasonable computational cost, the proper orthogonal decomposition technique is applied to reduce the model dimensions. Finally, the modeling strategy is validated against experimental results from the creasing test.The result of this project is a simulation tool, that is enables the description of the material behavior of paper in an efficient and robust manner while simultaneously accounting for the microscale effects. Moreover, a deeper understanding is generated on how the different effects on the fiber and network level interact, which is impossible with purely experimental investigations.