Wang Wei, Liu Yang, Xie Zongwu
State Key Laboratory of Robotics and Systems, Harbin Institute of Technology, Harbin 150001, China.
Polymers (Basel). 2023 Jul 26;15(15):3172. doi: 10.3390/polym15153172.
Given the importance of hyperelastic constitutive models in the design of engineering components, researchers have been developing the improved and new constitutive models in search of a more accurate and even universal performance. Here, a modified hyperelastic constitutive model based on the Yeoh model is proposed to improve its prediction performance for multiaxial deformation of hyperelastic polymeric materials while retaining the advantages of the original Yeoh model. The modified constitutive model has one more correction term than the original model. The specific form of the correction term is a composite function based on a power function represented by the principal stretches, which is derived from the corresponding residual strain energy when the Yeoh model predicts the equibiaxial mode of deformation. In addition, a parameter identification method based on the cyclic genetic-pattern search algorithm is introduced to accurately obtain the parameters of the constitutive model. By applying the modified model to the experimental datasets of various rubber or rubber-like materials (including natural unfilled or filled rubber, silicone rubber, extremely soft hydrogel and human brain cortex tissue), it is confirmed that the modified model not only possesses a significantly improved ability to predict multiaxial deformation, but also has a wider range of material applicability. Meanwhile, the advantages of the modified model over most existing models in the literatures are also demonstrated. For example, when characterizing human brain tissue, which is difficult for most existing models in the literature, the modified model has comparable predictive accuracy with the third-order Ogden model, while maintaining convexity in the corresponding deformation domain. Moreover, the effective prediction ability of the modified model for untested equi-biaxial deformation of different materials has also been confirmed using only the data of uniaxial tension and pure shear from various datasets. The effective prediction for the untested equibiaxial deformation makes it more suitable for the practice situation where the equibiaxial deformation of certain polymeric materials is unavailable. Finally, compared with other parameter identification methods, the introduced parameter identification method significantly improves the predicted accuracy of the constitutive models; meanwhile, the uniform convergence of introduced parameter identification method is also better.
鉴于超弹性本构模型在工程部件设计中的重要性，研究人员一直在开发改进的和新的本构模型，以寻求更准确甚至通用的性能。在此，提出了一种基于Yeoh模型的改进超弹性本构模型，以提高其对超弹性聚合物材料多轴变形的预测性能，同时保留原始Yeoh模型的优点。改进后的本构模型比原始模型多一个修正项。修正项的具体形式是基于主伸长表示的幂函数的复合函数，它是从Yeoh模型预测等双轴变形模式时的相应残余应变能推导出来的。此外，引入了一种基于循环遗传模式搜索算法的参数识别方法，以准确获得本构模型的参数。通过将改进后的模型应用于各种橡胶或类橡胶材料（包括天然未填充或填充橡胶、硅橡胶、极软水凝胶和人脑皮层组织）的实验数据集，证实了改进后的模型不仅具有显著提高的多轴变形预测能力，而且具有更广泛的材料适用性。同时，也证明了改进后的模型相对于文献中大多数现有模型的优势。例如，在表征脑组织时，这对文献中的大多数现有模型来说是困难的，改进后的模型与三阶Ogden模型具有相当的预测精度，同时在相应的变形域中保持凸性。此外，仅使用来自各种数据集的单轴拉伸和纯剪切数据，也证实了改进后的模型对不同材料未经测试的等双轴变形具有有效的预测能力。对未经测试的等双轴变形的有效预测使其更适合于某些聚合物材料等双轴变形不可用的实际情况。最后，与其他参数识别方法相比，引入的参数识别方法显著提高了本构模型的预测精度；同时，引入的参数识别方法的均匀收敛性也更好。
