In this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

在这项工作中，分析了许多选定的、各向同性的、基于不变量的超弹性模型。所考虑的超弹性本构关系包括Gent(G)及其扩展模型，即所谓的广义Gent模型(GG)、指数幂律模型(Exp-PL)和幂律模型(PL)。所研究模型的材料参数已针对八个不同的实验数据集确定。正如已经证明的那样，著名的根特模型并不总是允许获得可接受的实验数据近似质量。此外，据观察，当满足 Rivlin 和 Saunders 提出的实验得出的条件时，通常会实现最佳的曲线拟合质量。然而，结果表明，Rivlin 和 Saunders 的条件与储能多凸性的数学要求相矛盾。假设多凸存储能量函数是为了确保存在正确定义的边界值问题的解并避免非物理材料响应。发现在分析的超弹性模型的情况下，多凸性条件的应用只会导致曲线拟合质量略有下降。当假定能量多凸性时，通常会为 PL 模型获得最佳的实验数据近似值。在非多凸超弹性模型中，GG 模型最常获得最佳曲线拟合结果。然而，结果表明，由于锁定效应的存在，G 和 GG 模型都存在问题。