In this work, large deformation of incompressible, hyperelastic membranes based on the quasi-linear viscoelasticity (QLV) theory is formulated. Time integration algorithm and the expression for consistent fourth-order tangent tensor are presented. The formulation covers isotropic as well as anisotropic polymeric and biological materials. To solve numerical examples, a nonlinear finite element formulation in the Lagrangian framework is developed. Finally, several examples are provided to investigate the applicability of the present formulation. It is found that the numerical results are in good agreement with the analytical and experimental results available in the literature.

中文翻译：

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基于准线性粘弹性理论的不可压缩膜的时变响应

在这项工作中，基于准线性粘弹性 (QLV) 理论制定了不可压缩超弹性膜的大变形。给出了时间积分算法和一致四阶正切张量的表达式。该配方涵盖各向同性以及各向异性聚合物和生物材料。为了解决数值示例，开发了拉格朗日框架中的非线性有限元公式。最后，提供了几个例子来研究本配方的适用性。发现数值结果与文献中可用的分析和实验结果非常吻合。