论文标题
纤维增强水凝胶的孔弹性模型的均质化
Homogenization of a Poroelasticity Model for Fibre-Reinforced Hydrogels
论文作者
论文摘要
在本文中，考虑了纤维增强水凝胶的水力机械反应的毛弹性模型的分析和均质化。在这里，所讨论的培养基被认为是一种高度异质的两部分培养基，该培养基由与水凝胶的定期分布的连接的纤维 - 损伤组成。虽然假定纤维是弹性的，但通过\ emph {biot的毛弹性}对水凝胶的液压反应进行建模。我们表明，由此产生的数学问题接受了独特的弱解决方案，并研究了解决级别参数的解决方案的极限行为（在两尺度收敛的意义上），表征了培养基的异质性。让这个量表参数趋于零，我们得出了一个有效的模型，其中孔隙压力的微变化在宏观尺度上产生了微应力校正。
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.
