Coupled diffusion of solvent molecules and mechanical stretching of polymeric networks induced swelling/deswelling in polymeric gels contributes to the ability of its “smart response” and “environmental sensitivity.” In this article, the coupled diffusion and large deformation of polymeric gels are clarified into three kinds of deformation conditions which all involve swelling/deswelling. The real numerical challenge is identified for simulating swelling/deswelling induced deformation of gels by solving the partial deferential control equation of a popular monophase model for gels in steady equilibrium state with a standard process of numerical discretization. To address the numerical challenge, a generalized decoupling numerical framework is developed based on a multiplicative decomposition of deformation gradient. The proposed framework is more flexible and works for almost all cases of deformation of gels no matter involving swelling/deswelling or not. Its element‐free implementation is also developed using the element‐free IMLS‐Ritz method and is validated through analyzing the three‐dimensional stable and unstable large deformation of the constrained gel cube and tube.

中文翻译：

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聚合物凝胶的广义解耦数值框架及其无元素实现

溶剂分子的扩散和聚合物网络的机械拉伸耦合导致聚合物凝胶中的溶胀/溶胀，有助于其“智能响应”和“环境敏感性”的能力。在本文中，聚合物凝胶的耦合扩散和大变形被阐明为三种变形条件，它们都涉及溶胀/溶胀。通过用标准的数值离散化方法解决稳态平衡状态下流行的单相凝胶模型的偏微分控制方程，可以确定模拟凝胶的溶胀/溶胀引起的真实数值挑战。为了解决数值挑战，基于变形梯度的乘法分解，开发了一个通用的解耦数值框架。所提出的框架更灵活，并且几乎适用于所有凝胶变形情况，无论是否涉及溶胀/溶胀。它的无元素实现也使用无元素IMLS-Ritz方法开发，并通过分析约束凝胶立方体和管的三维稳定和不稳定大变形进行了验证。