Swelling involving (extremely) large deformations simulations have wide range of applications in biomedicine, tissue engineering and hygienic product design. Typically, standard FEM is used in which deformations and chemical potential are chosen to be the prime variables. On the other hand, mixed hybrid finite element method (MHFEM) featuring an additional independent variable field flux possesses local mass conservation property. Such a property has shown its success in Darcy’s type equations with heterogeneous permeability. In this work, we perform a full-round comparison between MHFEM and FEM in solving swelling problems involving large deformations. Specifically, based on the permeability distributions, the problems fall into three categories: constant permeability, strain-dependent permeability and permeability with a discontinuous interface. For each category, we compare the two methods in aspects like solution convergence robustness, deformation, chemical potential and flux field accuracy and computational cost. We conclude that MHFEM outperforms standard FEM in terms of solution convergence robustness and the accuracy of all three fields when a swelling problem involves discontinuous interface in permeability.

中文翻译：

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在涉及极大变形的膨胀模拟中比较混合混合有限元方法与标准 FEM

涉及（极）大变形模拟的膨胀在生物医学、组织工程和卫生产品设计中具有广泛的应用。通常，使用标准 FEM，其中选择变形和化学势作为主要变量。另一方面，具有附加独立可变场通量的混合混合有限元方法 (MHFEM) 具有局部质量守恒特性。这种性质已在具有非均质渗透率的达西型方程中显示出其成功。在这项工作中，我们对 MHFEM 和 FEM 在解决涉及大变形的膨胀问题方面进行了全面比较。具体而言，基于渗透率分布，问题分为三类：恒定渗透率、应变相关渗透率和具有不连续界面的渗透率。对于每个类别，我们在解收敛鲁棒性、变形、化学势和通量场精度以及计算成本等方面比较了两种方法。我们得出结论，当膨胀问题涉及渗透率的不连续界面时，MHFEM 在求解收敛稳健性和所有三个场的准确性方面优于标准 FEM。