A new model is constructed to validate a non-linear elastic response of rubber-like materials. The proposed model is phenomenological and is the combination of Rivlin expression truncated in invariant \(\mathop I\nolimits_{1}\) with a term in \(\mathop I\nolimits_{2}\) coming from the Hart-Smith model and which has been modified by Gornet et al. This model has five rheological parameters adjusted with a genetic algorithm. The genetic algorithm method is used in binary code and two sets of experimental data (Treloar data and Nunes and Moreira data) from the literature to compare the proposed model. With Treloar rubber data the simple tension suffices for the determination of the parameter values. Thus, the fit of experimental data is 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, the proposed model has given direct material parameters in simple shear with good correlation. On the other hand, a comparison is made between the proposed model and the Beda model (2007), Gornet et al. model and hybrid integral approach (HIA) model. The proposed model is the most efficient among three other classical models because the proposed model emerges from very small relative errors with Treloar's experimental data: 0.42 ± 0.08 in simple tension, 0.44 ± 0.07 in biaxial tension and 0.42 ± 0.05 in pure shear. This model also incorporates all the criteria for model validation described in the literature.

中文翻译：

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各向同性材料大弹性变形中应变能的现象学表达。

构建了一个新模型来验证类橡胶材料的非线性弹性响应。所提出的模型是现象​​学的，并且是在不变\（\ mathop I \ nolimits_ {1} \）中截取的Rivlin表达与\（\ mathop I \ nolimits_ {2} \）中的术语的组合来自Hart-Smith模型，并已由Gornet等修改。该模型具有通过遗传算法调整的五个流变参数。遗传算法方法用于二进制代码和文献中的两组实验数据（Treloar数据以及Nunes和Moreira数据）以比较所提出的模型。使用Treloar橡胶数据，简单的张力就足以确定参数值。因此，实验数据的拟合显示出在使用相同的材​​料参数集的情况下，在双轴拉伸和纯剪切作用下可提供准确的响应和预测性描述。与莫雷拉数据不同，所提出的模型在简单剪切中给出了直接的材料参数，具有良好的相关性。另一方面，Gornet等人在提出的模型与Beda模型（2007年）之间进行了比较。模型和混合积分法（HIA）模型。所提出的模型是其他三个经典模型中效率最高的模型，因为所提出的模型是根据Treloar的实验数据产生的相对较小的误差得出的：简单张力为0.42±0.08，双轴张力为0.44±0.07，纯剪切力为0.42±0.05。该模型还结合了文献中描述的所有模型验证标准。