反应诱导聚合物双层结构弯曲行为的建模与分析

Modeling and Analysis of Bending Behavior of Polymer Bilayers Caused by Chemical Reaction

聚合物软材料兼具柔软性和大变形能力,作为一种智能材料在软体机器人等领域应用广泛.化学活性聚合物分子内包含具有较高反应活性的官能团,如环氧、酯键、羟基、羧基等,可以在一定条件下发生化学反应引起材料体积和性质变化.因此研究化学反应如何调控聚合物变形对开发新的功能型聚合物材料有重要指导意义.本文建立化学活性聚合物-弹性基底双层结构的理论模型并分析其在化学反应诱导下的有限弯曲行为.引入化学反应进度作为Helmholtz自由能独立的状态变量,考虑化学反应对聚合物体积变化和模量的影响,以及反应过程独立的能量耗散机制,并基于Neo-Hookean模型建立起各层内的超弹性本构关系.最后利用Newton-Raphson方法对反应完全时的平面应变稳态问题进行数值求解,得到不同几何和反应影响参数下各层内的弯曲变形和应力分布.

Soft polymers have both flexibility and large-deformation capability, and are widely used as smart materials in fields such as soft robotics. The chemo-active polymers contain highly reactive functional groups, such as epoxy, ester bonds, hydroxyl groups, and carboxyl groups, which can undergo chemical reactions under certain conditions and change volumes and properties of polymers. Therefore, to design new functional polymers, it is significant to study how the chemical reaction regulates deformation in chemo-active polymers. Here we establish a theoretical model of a chemo-active polymer-elastomer bilayer and analyze its finite bending behavior caused by a chemical reaction. The extent of the chemical reaction is introduced as an independent state variable in the Helmholtz free energy and the influences of reaction on the volume change and modulus are considered in this paper; meanwhile an independent energy dissipation mechanism of the chemical reaction is also established, then we establish the hyperelastic constitutive relation in each layer based on the Neo-Hookean model. Finally, the steady-state plane strain problem at the end of reaction is solved numerically by Newton-Raphson method and the distributions of bending deformation and stress in each layer under different geometric and reaction-influenced parameters are obtained.