ABSTRACT The choice of an appropriate strain energy function W is key to accurate modeling and computational finite element analysis of the mechanical behavior of unfilled non-crystalizing rubberlike materials. Despite the existing variety of models, finding a suitable model that can capture many deformation modes of a rubber specimen with a single set of parameter values and satisfy the a priori mathematical and structural requirements remains a formidable task. Previous work proposed a new generalized neo-Hookean W (I1) function, showing a promising fitting capability and enjoying a structural basis. We now use two extended forms of that model that include an I1 term adjunct, W (I1, I2), for application to various boundary value problems commonly encountered in rubber mechanics applications. Specifically, two functional forms of the I2 invariant are considered: a linear function and a logarithmic function. The boundary value problems of interest include the in-plane uniaxial, equi-biaxial, and pure shear deformations and simple shear, inflation, and nonhomogeneous deformations such as torsion. By simultaneous fitting of each model to various deformation modes of rubber specimens, it is demonstrated that a single set of model parameter values favorably captures the mechanical response for all the considered deformations of each specimen. It is further shown that the model with a logarithmic I2 function provides better fits than the linear function. Given the functional simplicity of the considered W (I1, I2) models, the low number of model parameters (three in total), the structurally motivated bases of the models, and their capability to capture the mechanical response for various deformations of rubber specimens, the considered models are recommended as a powerful tool for practical applications and analysis of rubber elasticity.

中文翻译：

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评估一系列橡胶类材料和变形的新的各向同性超弹性本构模型

摘要 选择合适的应变能函数 W 是对未填充非结晶类橡胶材料的力学行为进行精确建模和计算有限元分析的关键。尽管现有的模型多种多样，但找到一个合适的模型，可以通过一组参数值捕获橡胶试样的多种变形模式并满足先验的数学和结构要求，仍然是一项艰巨的任务。以前的工作提出了一个新的广义新胡克 W (I1) 函数，显示出有前途的拟合能力并享有结构基础。我们现在使用该模型的两种扩展形式，包括 I1 项附加项 W (I1, I2)，用于解决橡胶力学应用中常见的各种边值问题。具体来说，考虑 I2 不变量的两种函数形式：线性函数和对数函数。感兴趣的边值问题包括平面内单轴、等双轴和纯剪切变形以及简单剪切、膨胀和非均匀变形（例如扭转）。通过将每个模型同时拟合到橡胶试样的各种变形模式，证明了一组模型参数值可以很好地捕捉每个试样的所有考虑变形的机械响应。进一步表明，具有对数 I2 函数的模型比线性函数提供更好的拟合。考虑到所考虑的 W (I1, I2) 模型的功能简单性、模型参数数量少（总共三个）、模型的结构动机基础，