主动应变驱动的位移跳跃现象的建模与仿真

Active-strain actuated snap-through phenomena, capable of generating extremely fast movements between different stable configurations, play essential roles in realizing specific functions for some plants, animals and engineering devices. It is of great importance to develop efficient numerical models to simulate such phenomena, because it will definitely help to trace the whole equilibrium path and thus benefits for the explanation of some natural phenomena and design of engineering devices. This project will first introduce a finite element (FE) model aiming to model the snap-through phenomena in soft matter actuated by prescribed initial strain, a simplification of the general active strain. With the effects of the initial strain considered, and a new equivalent body force can be obtained in the linearized FE equation. Based on the FE formulation, an equilibrium-path tracing algorithm, called the generalized Riks method, will be designed and used to simulate some typical devices with snap-through behaviors. Then, based on the developed generalized Riks method, A FE simulation framework capable of capturing the swelling-actuated snap-through in hydrogels will be developed, where the equivalent body force proportional to the increment of the chemical potential can be deduced and a quadratic equation related to the unknowns will be introduced to complete the linearized FE equation. The algorithm will be used to model the snap-through phenomena in hydrogel composites. Lastly, within the framework of developed algorithm, the snap-through behaviors actuated by anisotropic active strain will be investigated. The effects of the moduli and direction of fiber on the critical states in the snap-through phenomena of hydrogel devices will be illuminated.

由吸水膨胀、热膨胀等因素引起的主动应变可驱动特定结构产生位移跳跃失稳，实现不同稳定构型之间快速转换，对自然界生物及工程器件发挥特定功能起到重要作用。本项目旨在发展模拟主动应变驱动的位移跳跃行为的非线性有限元方法，以期为相关器件的设计提供可靠分析工具。首先，将不同因素引起的主动应变简化为指定初应变，导出相应的非线性有限元分析格式，得到线性化有限元方程中由初应变引起的非线性等效体积力一般形式，构造关于未知量的二次弧长方程，设计可自动跟踪平衡路径的广义Riks方法。其次，基于所发展的广义Riks方法基本思想，构建模拟水凝胶溶胀驱动的位移跳跃失稳行为的有限元方法，导出化学势变化引起的等效体积力的一般形式，研究单层、多层水凝胶复合薄膜的位移跳跃行为。最后，基于所开发通用分析模型，植入纤维增强型各向异性本构模型，研究各向异性溶胀驱动的位移跳跃行为，揭示纤维模量及方向对水凝胶结构位移跳跃行为的影响规律。

具有两个稳定状态的双稳态结构在自然界和工程中很常见，比如捕蝇草和双稳态作动器。在外力、温度变化、溶胀等刺激作用下，这类结构可从一个稳定状态快速转换至另一个稳定状态（即位移跳跃），在微作动器、能量收集装置、力学超材料等领域存在大量潜在应用。本项目针对双稳态结构及其位移跳跃行为，开展了理论、实验和数值研究工作，包括电压驱动的双稳态压电薄壁结构“位移跳跃”行为的有限元算法、电磁场驱动的双稳态作动器的实验、理论及应用、面内各向异性主动应变作用下双层结构的双稳态行为和最优折叠行为驱动策略、夹支弹性梁的双稳态特性、磁敏薄壁结构的理论分析和数值模拟以及带有几何缺陷的球壳的双稳态行为。所发展的基于Riks方法的有限元方法可应用于复合压电结构、带缺陷DWV球壳、夹支柔性梁、电磁敏感梁等形式的双稳态结构，模拟其位移跃过程中的非单调位移荷载路径，识别产生位移跳跃行为的临界荷载点。本项目所发展的磁敏双稳态预屈曲PDMS梁作为一种快速作动器，克服了传统的双稳态作动器响应速度慢、作动过程不易控制、高电压输入等缺陷，通过控制电流大小，可制备智能开关和弹跳器。针对不同形式的双稳态结构，包括夹支预屈曲弹性梁、各向异性主动应变驱动双层薄壁结构以及带缺陷的球壳，通过理论、实验和数值模拟，获得了决定其双稳态行为相图及不同稳态切换过程中位移-载荷平衡路径，所的得到的结果为设计高性能双层作动器和软机器提供了潜在的指导。所发展的电磁软材料大变形理论及基于Riks方法的路径跟踪方法，可模拟磁场作用下材料大变形及磁场重分布的强耦合行为，并捕捉磁场力作用下位移跳跃失稳行为。本项目针对双稳态结构及其位移跳跃行为的研究，将为双稳态的快速作动器、力学超材料、能量收集装置、微机电系统的设计提供理论依据和数值模拟工具。