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Level set based eXtended finite element modelling of the response of fibrous networks under hygroscopic swelling
arXiv - CS - Computational Engineering, Finance, and Science Pub Date : 2020-06-23 , DOI: arxiv-2006.14049
P. Samantray, R.H.J. Peerlings, E. Bosco, M.G.D. Geers, T.J. Massart, O. Roko\v{s}

Materials like paper, consisting of a network of natural fibres, exposed to variations in moisture, undergo changes in geometrical and mechanical properties. This behaviour is particularly important for understanding the hygro-mechanical response of sheets of paper in applications like digital printing. A two-dimensional microstructural model of a fibrous network is therefore developed to upscale the hygro-expansion of individual fibres, through their interaction, to the resulting overall expansion of the network. The fibres are modelled with rectangular shapes and are assumed to be perfectly bonded where they overlap. For realistic networks the number of bonds is large and the network is geometrically so complex that discretizing it by conventional, geometry-conforming, finite elements is cumbersome. The combination of a level-set and XFEM formalism enables the use of regular, structured grids in order to model the complex microstructural geometry. In this approach, the fibres are described implicitly by a level-set function. In order to represent the fibre boundaries in the fibrous network, an XFEM discretization is used together with a Heaviside enrichment function. Numerical results demonstrate that the proposed approach successfully captures the hygro-expansive properties of the network with fewer degrees of freedom compared to classical FEM, preserving desired accuracy.

中文翻译:

吸湿膨胀下纤维网络响应的基于水平集的扩展有限元建模

纸等材料由天然纤维网络组成,暴露在湿度变化的环境中,其几何和机械特性会发生变化。这种行为对于了解纸张在数字印刷等应用中的湿机械响应尤为重要。因此,开发了纤维网络的二维微结构模型,以通过它们的相互作用将单个纤维的湿膨胀放大到网络的整体膨胀。纤维以矩形形状建模,并假设在它们重叠的地方完美粘合。对于现实网络,键的数量很大,而且网络在几何上非常复杂,以至于通过传统的、符合几何形状的有限元对其进行离散化是很麻烦的。水平集和 XFEM 形式主义的结合可以使用规则的结构化网格来模拟复杂的微观结构几何。在这种方法中,纤维由水平集函数隐式描述。为了表示纤维网络中的纤维边界,XFEM 离散化与 Heaviside 富集函数一起使用。数值结果表明,与经典 FEM 相比,所提出的方法以更少的自由度成功捕获了网络的吸湿膨胀特性,同时保持了所需的精度。XFEM 离散化与 Heaviside 富集函数一起使用。数值结果表明,与经典 FEM 相比,所提出的方法以更少的自由度成功捕获了网络的吸湿膨胀特性,同时保持了所需的精度。XFEM 离散化与 Heaviside 富集函数一起使用。数值结果表明,与经典 FEM 相比,所提出的方法以更少的自由度成功捕获了网络的吸湿膨胀特性,同时保持了所需的精度。
更新日期:2020-06-26
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