纤维增强水凝胶多孔弹性模型的均匀化
Homogenization of a Poroelasticity Model for Fibre-Reinforced Hydrogels
AI总结：
本文研究了纤维增强水凝胶多孔弹性模型的均匀化，证明了弱解唯一性，并通过双尺度收敛获得含微观应力修正的有效宏观模型。
摘要：
本文考虑了纤维增强水凝胶水力力学响应的多孔弹性模型的分析与均匀化。此处，所讨论的介质被视为高度异质的双组分介质，由连通的纤维支架和周期性分布的水凝胶夹杂组成。假设纤维是弹性的，水凝胶的水力力学响应用Biot多孔弹性建模。我们证明了所得数学问题存在唯一的弱解，并研究了在表征介质异质性的尺度参数下，解的极限行为（在双尺度收敛意义下）。令该尺度参数趋于零，得到一个有效模型，其中孔隙压力的微观变化在宏观尺度上引起微观应力修正。
英文摘要：
In this paper, the analysis and homogenization of a poroelastic model for the hydro-mechanical response of fibre-reinforced hydrogels is considered. Here, the medium in question is considered to be a highly heterogeneous two-component media composed of a connected fibre-scaffold with periodically distributed inclusions of hydrogel. While the fibres are assumed to be elastic, the hydromechanical response of hydrogel is modeled via \emph{Biot's poroelasticity}. We show that the resulting mathematical problem admits a unique weak solution and investigate the limit behavior (in the sense of two-scale convergence) of the solutions with respect to a scale parameter, characterizing the heterogeneity of the medium. Letting this scale parameter tend to zero, we arrive at an effective model where the micro variations of the pore pressure give rise to a micro stress correction at the macro scale.
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