This research work is devoted to the improvement the Hybrid Integral Aproach (HIA) proposed by Nguessong et al. for the characterization of the nonlinear elastic response of rubber-like materials. The improvement is based on the choice of the approximation of the inverse Langevin function for the molecular part and on the modification of the second term I 2 for the phenomenological part. Thus, in the new proposed model, we retain the approximation of the inverse Langevin function defined by Marchi and Arruda to improve the first term which represents the molecular part. With this approximation, the relative error is very minimal (0.0015%) compared to the others approximation existing. The second term of this proposed model comes from the Gornet et al. model. This model contents six rheological parameters optimized by the Levenberg-Marquardt method. Two sets of experimental data (Treloar data and Nunes and Moreira data), from the literature, are used to compare this proposed model with initial HIA model. With Treloar rubber, data the simple tension suffice to determine the parameter values. Thus, the fit of the experimental data has been shown to provide an accurate response and predictive description in biaxial tension and pure shear with the same sets of material parameters. Unlike with Moreira data, this proposed model gives directly the material parameters in simple shear with good correlation. On the other hand, comparison is made between the proposed model and the HIA model. The proposed model is most efficient, because the proposed model emerges from a very small relative errors with Treloar’s experimental data: 0.01 0. 0.04 in simple tension, 0.02 ± 0.006 in biaxial tension and 0.07 ± 0.005 in pure shear.

中文翻译：

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马尔奇和阿鲁达提出的 HIA 模型的改进和逆朗之万函数的影响

这项研究工作致力于改进 Nguessong 等人提出的混合积分方法（HIA）。用于表征橡胶类材料的非线性弹性响应。改进是基于对分子部分的逆朗之万函数的近似选择和对现象学部分的第二项 I 2 的修改。因此，在新提出的模型中，我们保留了由 Marchi 和 Arruda 定义的逆朗之万函数的近似值，以改进代表分子部分的第一项。使用此近似值，与现有的其他近似值相比，相对误差非常小 (0.0015%)。该模型的第二项来自 Gornet 等人。模型。该模型包含通过 Levenberg-Marquardt 方法优化的六个流变参数。来自文献的两组实验数据（Treloar 数据和 Nunes 和 Moreira 数据）用于将这个提议的模型与初始 HIA 模型进行比较。对于 Treloar 橡胶，数据简单的张力足以确定参数值。因此，实验数据的拟合已被证明可以在具有相同材料参数集的双轴拉伸和纯剪切中提供准确的响应和预测描述。与 Moreira 数据不同，该模型直接给出了简单剪切下的材料参数，并具有良好的相关性。另一方面，对所提出的模型和 HIA 模型进行了比较。所提出的模型是最有效的，因为所提出的模型与 Treloar 的实验数据的相对误差非常小：简单张力为 0.01 0. 0.04，双轴张力为 0.02 ± 0.006 和 0.