In this paper, a solid-shell finite element method for the inhomogeneous swelling of anisotropic thin-walled hydrogels with reinforced fibers is developed. In this numerical framework, the anisotropic mechanical deformation of fiber-reinforced hydrogels is driven by solvent diffusion. The solid-shell model including only displacement degree of freedom is developed for anisotropic hydrogels. The model can directly incorporate three-dimensional material laws based on the modified Flory-Rehner theory for anisotropic thin-walled hydrogels and bypass complex update algorithms for the normal vector in conventional shell models. The constitutive relation and the corresponding tangent moduli for anisotropic hydrogels, referring to convected coordinate system, are derived according to the modified material model. The weak form of equilibrium equation is derived based on the three-field variational principle. Moreover, enhanced assumed strain and assumed natural strain methods are adopted to avoid Poisson-thickness locking and shear locking encountered in simulations of thin-walled hydrogels with reinforced fibers, respectively. Finally, two representative examples considering various moduli and initial directions of fibers are presented to verify the validity, accuracy and efficiency of the proposed method. The applications to predict the swelling of flowers demonstrate that the solid-shell based method for anisotropic swelling of soft materials can assist design of bionic devices.

本文提出了一种固体壳有限元方法，用于各向异性增强纤维薄壁水凝胶的不均匀膨胀。在此数值框架中，纤维增强水凝胶的各向异性机械变形是由溶剂扩散驱动的。为各向异性水凝胶开发了仅包含位移自由度的固体模型。该模型可以基于修正的Flory-Rehner理论将各向异性的薄壁水凝胶直接纳入三维材料定律，并在常规壳模型中绕过法向矢量的复杂更新算法。根据改进的材料模型，导出了对流坐标系下各向异性水凝胶的本构关系和相应的切线模量。根据三场变分原理推导了平衡方程的弱形式。此外，采用增强的假定应变和假定的自然应变方法分别避免了在具有增强纤维的薄壁水凝胶的模拟中遇到的泊松厚度锁定和剪切锁定。最后，给出了考虑纤维的各种模量和初始方向的两个代表性实例，以验证所提方法的有效性，准确性和效率。预测花朵膨胀的应用表明，基于固体的软材料各向异性膨胀方法可以帮助仿生设备的设计。分别采用增强的假定应变和假定的自然应变方法来避免在具有增强纤维的薄壁水凝胶的模拟中遇到的泊松厚度锁定和剪切锁定。最后，给出了考虑纤维的各种模量和初始方向的两个代表性实例，以验证所提方法的有效性，准确性和效率。预测花朵膨胀的应用表明，基于固体的软材料各向异性膨胀方法可以帮助仿生设备的设计。分别采用增强的假定应变和假定的自然应变方法来避免在具有增强纤维的薄壁水凝胶的模拟中遇到的泊松厚度锁定和剪切锁定。最后，给出了考虑纤维的各种模量和初始方向的两个代表性实例，以验证所提方法的有效性，准确性和效率。预测花朵膨胀的应用表明，基于固体的软材料各向异性膨胀方法可以帮助仿生设备的设计。