基于开源有限元的水凝胶力学行为研究

STUDY ON MECHANICAL BEHAVIOR OF HYDROGELS BASED ON OPEN SOURCE FINITE ELEMENT CODE

章肖阳

11849100

硕士

航天工程

洪伟

2020-05-28

2020-07-13

哈尔滨工业大学

深圳

本课题的内容主要围绕聚合物凝胶溶胀的非平衡态热力学理论模型展开， 并针对凝胶在溶胀和退溶胀过程中模量随高分子体积分数变化的标度律加以修 正，利用开源有限元平台结合上述理论研究了一些有趣的凝胶溶胀现象。 对于化学凝胶溶胀的非平衡态热力学理论，回顾介绍了经典的化学凝胶溶 胀理论，在此基础上推导出有限元建模的控制方程，并在开源平台 FEniCS 上 实现了凝胶溶胀仿真程序。其次，本课题还将最近发表的水凝胶溶胀与退溶胀 过程中的标度律扩展到描述复杂构型凝胶结构在力化学耦合作用下行为的连续 介质场论，并进行了有限元实现。 将开源有限元平台 FEniCS 应用于研究上述化学凝胶溶胀的非平衡态热力 学理论，利用上述推导出有限元建模的控制方程建立相关的 FEniCS 化学凝胶 溶胀模型，并在上述程序的基础上进行扩展应用：将标度律修正的水凝胶场论 应用到化学凝胶溶胀 FEniCS 二维模型中，与经典 Flory-Huggins 理论以及 COMSOL 模型的结果进行比较；结合 FEniCS 建模研究水凝胶薄膜溶胀过程中 的起皱现象；结合 FEniCS 建模研究不对称截面化学凝胶长条溶胀动力学行为。 FEniCS 非常适合处理多物理场耦合的有限元问题，相比商用软件，其主 要优势是开放性、支持高性能并行运算、并内置多种求解器，开源自定义的形 式可以让研究者对所研究问题的理论有更深刻的认识，非常适合用于教学与科 研。在过去的十年中，大量的研究人员致力于提高水凝胶性能，使其在生物医 学、柔性电子、传感器和致动器等众多领域的应用机会大大增加。研究水凝胶 的溶胀的理论模型以及基于理论的数值模型与仿真工具对扩展水凝胶的应用而 言非常重要。此研究将不同领域的先进技术结合起来，致力于提高水凝胶的力 学性能、设计制造更实用的结构，引进一些新的功能，并结合其工程实际应用， 推动水凝胶研究的进一步创新发展。

This study mainly focuses on the field theory of polymeric gels based on non- equilibrium thermodynamics, and a modification by considering a recently proposed scaling law between the modulus and polymer volume fraction during swelling and deswelling. A series of interesting phenomena of hydrogels and gel structures have been studied by implementing the field theory on an open source finite element platform, FEniCS. This thesis first reviews the non-equilibrium thermodynamics of gel swelling and the derivation of the governing equation for the continuum field theory, which was used to implement a finite element code on FEniCS. Secondly, a recently proposed scaling law between the elastic modulus and the polymer volume fraction of swelling and deswelling hydrogels is extended into a free energy function, and then implemented into the finite element code. The open source finite element platform, FEniCS, was applied to study the swelling and deformation of polymeric gels. Several examples are used to verify the numerical code and to demonstrate the applications of the model: (1) swelling and deswelling process by applying a model consistent with the scaling law; (2) the wrinkling instability in a double-layer gel structure; (3) the kinetics-induced peculiar bending phenomenon of a 3D-printed hydrogel strip with asymmetric section. FEniCS is suitable for multi-physics multi-field coupled problems. Major advantages of FEniCS include the support of high-performance parallel computation and a variety of built-in solvers. The open-source platform and user-friendly language allow researchers to focus more on the physical problems, and are very suitable for research as well as teaching. Over the past decade, a large number of researchers have focused on improving the mechanical performance of hydrogels, and developing applications in biomedical, flexible electronics, sensors and actuators. The theoretical studies on the behaviors of hydrogels and physics-based models and numerical tools are essential to the development of these applications. Scientists are committed to improving the mechanical properties of hydrogels, designing and manufacturing more practical structures, introducing some new functions, and to promoting engineering applications of hydrogels by combining the advanced technologies from different fields.

水凝胶 有限元 FEniCS 标度律 褶皱

hydrogel finite element FEniCS scaling law wrinkle

中文

联合培养

南方科技大学

章肖阳. 基于开源有限元的水凝胶力学行为研究[D]. 深圳. 哈尔滨工业大学,2020.