（PDMS）-石墨烯弹性体纳米复合材料的机电耦合和压电行为

摘要(中文译文)

基于弹性体的纳米复合材料将聚合物的柔性与导电纳米填料相结合，提供了轻质、可拉伸且机电性能可调的系统，适用于可穿戴电子器件、软体机器人和自供电传感器。然而，预测其非线性响应仍然具有挑战性，因为所观察到的类压电响应源于应变依赖的界面极化以及非均质微结构中不断演化的压阻传导路径。我们提出了一种连续介质电-超弹性框架，将用于大应变弹性行为的Mooney-Rivlin模型与用于静电耦合的Helmholtz自由能方法相结合。推导了应力、电位移和表观压电系数的解析表达式，并将其应用于有限元模拟中。该模型准确再现了含0.1-1 wt%石墨烯的聚二甲基硅氧烷（PDMS）纳米复合材料的实验力学、介电和机电行为。这些材料表现出刚度、相对介电常数（从3.4增至4.0，约18%）以及准静态d系数（从-5.6增至-10.0 pC N，约80%提升）的增加。解析与有限元法（FEM）结果在整个变形范围内显示出一致的趋势，在较低变形水平下Maxwell应力吻合度在10%以内，而在轴向位移u = ~-1 mm（约16.7%压缩应变）时，耦合机电量的偏差为33-40%，这归因于单轴解析假设中不存在的三维剪切效应。模拟表明，石墨烯增强了Maxwell应力，在较低拉伸比下产生四倍增长。这将PDMS-石墨烯复合材料重新定义为电-超弹性材料，提供了一个具有预测性且可扩展的框架。它突显了表观压电性作为一种涌现的、可调效应，源于柔性超弹性基体中的电荷重新分布——从而指导下一代柔性器件的设计，使其利用场诱导耦合而非固有极化。

Abstract

Elastomer-based nanocomposites combining polymer flexibility with conductive nanofillers provide lightweight, stretchable systems with tunable electromechanical properties for wearable electronics, soft robotics, and self-powered sensors. However, predicting their nonlinear response remains challenging because the observed piezoelectric-like response arises from strain-dependent interfacial polarization and evolving piezoresistive conduction pathways within heterogeneous microstructures. We introduce a continuum electro-hyperelastic framework combining the Mooney-Rivlin model for large-strain elasticity with a Helmholtz free-energy approach for electrostatic coupling. Analytical expressions for stress, electric displacement, and apparent piezoelectric coefficients are derived and implemented in finite element simulations. The model accurately reproduces the experimental mechanical, dielectric, and electromechanical behaviour of polydimethylsiloxane (PDMS) nanocomposites with 0.1-1 wt% graphene. These show increased stiffness, relative permittivity (from 3.4 to 4.0, ≈18%), and quasi-static d coefficients (from -5.6 to -10.0 pC N, ≈80% enhancement). Analytical and finite element method (FEM) results show consistent trends across the full deformation range, with Maxwell stress agreement within 10% at lower deformation levels, while deviations of 33-40% for coupled electromechanical quantities at an axial displacement u = ~-1 mm (~16.7% compressive strain) are attributable to three-dimensional shear effects absent from the uniaxial analytical assumption. Simulations reveal that graphene boosts Maxwell stress, yielding a four-fold increase at lower stretch ratios. This reframes PDMS-graphene composites as electro-hyperelastic materials, offering a predictive, extensible framework. It highlights apparent piezoelectricity as an emergent, tunable effect from charge redistribution in a compliant hyperelastic matrix-guiding the design of next-generation flexible devices leveraging field-induced coupling over intrinsic polarization.

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