Swelling pressure in the interstitial fluid within the pores of cartilage tissue is known to have a significant effect on the rheology of cartilage tissue. The swelling pressure varies rapidly within thin regions inside pores known as Debye layers, caused by the presence of fixed charge, as observed in cartilage. Tissue level calculation of cartilage deformation therefore requires resolution of three distinct spatial scales: the Debye lengthscale within individual pores; the lengthscale of an individual pore; and the tissue lengthscale. We use asymptotics to construct a leading order approximation to the swelling pressure within pores, allowing the swelling pressure to be systematically included within a fluid-solid interaction model at the level of pores in cartilage. We then use homogenization to derive tissue level equations for cartilage deformation that are very similar to those governing the finite deformation of a poroviscoelastic body. The equations derived permit the spatial variations in porosity and electric charge that occur in cartilage tissue. Example solutions are then used to confirm the plausibility of the model derived and to consider the impact of fixed charge heterogeneity, illustrating that local fixed charge loss is predicted to increase deformation gradients under confined compression away from, rather than at, the site of loss.

中文翻译：

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在软骨变形的组织水平多孔弹性模型中对溶胀压力进行建模。

已知在软骨组织的孔内的间质液中的溶胀压力对软骨组织的流变性具有显着影响。如在软骨中所观察到的，由于固定电荷的存在，溶胀压力在称为Debye层的孔内的薄区域内迅速变化。因此，计算软骨变形的组织水平需要解析三个不同的空间尺度：单个孔内的德拜长度尺度；以及 单个孔的长度尺度；和组织的长度尺度。我们使用渐近线构造毛孔内溶胀压力的前导近似值，使溶胀压力被系统地包含在软骨孔内液-固相互作用模型中。然后，我们使用均质化来得出软骨变形的组织水平方程，该方程与控制多孔弹性体的有限变形的方程非常相似。导出的等式允许在软骨组织中发生的孔隙率和电荷的空间变化。然后使用示例解决方案来确认导出的模型的合理性并考虑固定电荷异质性的影响，这说明局部固定电荷损失预计将在有限压缩下远离损失位置而不是在损失位置增加变形梯度。