通过渐近均匀化和与理想模型的比较研究纸纤维网络的湿力学性质
Hygro-mechanical properties of paper fibrous networks through asymptotic homogenization and comparison with idealized models
摘要：
本文提出了一种多尺度的方法来预测纸张的有效湿力学行为的基础上的纤维网络的属性。尽管有大量的文献对纸张湿膨胀，功能依赖的有效材料性能的微观结构特征仍然不清楚。在这项工作中，纸纤维网络的微观结构模型首先开发的随机沉积的平面区域内的纤维根据取向概率密度函数。渐近均匀化是用来确定其有效的性质数值。或者，两个更理想化的微观结构模型被认为是，一个基于一个定期的晶格结构与一个规则的网络的垂直纤维和一个基于Voigt平均。尽管它们简单，但它们再现了代表性的微观结构特征，例如取向各向异性和网络水平的湿弹性特性。这些替代模型可以解析求解，提供封闭形式的表达式，明确揭示了有效的湿力学响应的个别微观尺度参数的影响。随机网络模型预测的趋势被两个理想化模型合理地捕捉到。所得的湿力学性能最后与文献中报道的实验数据进行比较，揭示了足够的定量协议。
英文摘要：
This paper presents a multi-scale approach to predict the effective hygro-mechanical behaviour of paper sheets based on the properties of the underlying fibrous network. Despite the vast amount of literature on paper hygro-expansion, the functional dependence of the effective material properties on the micro-structural features remains yet unclear. In this work, a micro-structural model of the paper fibrous network is first developed by random deposition of the fibres within a planar region according to an orientation probability density function. Asymptotic homogenization is used to determine its effective properties numerically. Alternatively, two much more idealized micro-structural models are considered, one based on a periodic lattice structure with a regular network of perpendicular fibres and one based on the Voigt average. Despite their simplicity, they reproduce representative micro-structural features, such as the orientation anisotropy and network level hygro-elastic properties. These alternative models can be solved analytically, providing closed-form expressions that explicitly reveal the influence of the individual micro-scale parameters on the effective hygro-mechanical response. The trend predicted by the random network model is captured reasonably well by the two idealized models. The resulting hygro-mechanical properties are finally compared with experimental data reported in the literature, revealing an adequate quantitative agreement.
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