To describe the specific behavior of soft biological tissues that can be regarded as incompressible, a strain energy function for fiber-reinforcement materials based on two isotropic and anisotropic deformation invariants is developed and investigated. The anisotropic properties of simple composite materials were initially studied and now extensive hyperelastic modeling is used to analyze the dynamic characteristics of a dielectric elastomer membrane that experiences finite strains and is reinforced by one family of fiber. It should be noted that the presence of fibers in the rubber matrix will strengthen the structure, but here the presence of fibers will greatly reduce the electric field required to activate the dielectric elastomer and thus be stimulated with a lower voltage. It even helps to reduce the issue of instability that is a common thing in dielectric elastomers. Therefore, the effect of fiber angle orientation in an anisotropic dielectric elastomer under combined loads of biaxial tensile forces and an electric field with a focus on the damping effects is completely studied for different cases. Based on the Gent model, phase diagrams, dynamic response diagrams, and resonance frequency diagrams are also plotted for several values of fibers directions and damping coefficients.

中文翻译：

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纤维结构对各向异性介电弹性体膜非线性振动的影响

为了描述可被视为不可压缩的软生物组织的特定行为，开发并研究了基于两个各向同性和各向异性变形不变量的纤维增强材料的应变能函数。最初研究了简单复合材料的各向异性特性，现在使用广泛的超弹性模型来分析介电弹性体膜的动态特性，该膜经历有限应变并由一类纤维增强。应该注意的是，橡胶基质中纤维的存在会加强结构，但这里纤维的存在会大大降低激活介电弹性体所需的电场，从而用较低的电压进行刺激。它甚至有助于减少介电弹性体中常见的不稳定性问题。因此，针对不同情况，对各向异性介电弹性体在双轴拉伸力和电场的联合载荷下纤维角度取向的影响进行了全面研究，重点是阻尼效应。基于 Gent 模型，还绘制了多个纤维方向和阻尼系数值的相图、动态响应图和共振频率图。