The present paper proposes a new Strain Energy Function (SEF) for incompressible transversely isotropic hyperelastic materials, i.e. materials with a single fiber family. This SEF combines polyconvex invariants forming an integrity basis (Ta et al., 2014) in a polynomial and exponential form. Compared to a previous attempt for building a SEF based on the same invariants (Cai et al., 2016), we have reduced the number of material parameters from 23 to 10, without losing any accuracy on the numerical results. The 10 material parameters are identified by comparing the closed form solutions deriving from our model with experimental and numerical data extracted from the literature. These data concern uniaxial tension and shear tests, both parallel and transverse to the fiber direction (Ciarletta et al., 2011; Davis and De Vita, 2014) [3, 4], as well as shear calculations with 9 different fiber angles (Horgan and Murphy, 2017) [5]. Due to the variety of the considered situations, we have developed specific identification strategies based on: 1) the linear or nonlinear nature of the material parameters of the model; 2) the modeling of the free boundary conditions by a spectral approach.

本论文为不可压缩的横向各向同性超弹性材料（即具有单纤维族的材料）提出了一种新的应变能函数 (SEF)。该 SEF 以多项式和指数形式组合了多凸不变量，形成了完整性基础（Ta 等人，2014 年）。与之前基于相同不变量构建 SEF 的尝试（Cai 等人，2016 年）相比，我们将材料参数的数量从 23 个减少到 10 个，而不会损失任何数值结果的准确性。通过比较从我们的模型得出的封闭形式解与从文献中提取的实验和数值数据，确定了 10 个材料参数。这些数据涉及平行和横向于纤维方向的单轴拉伸和剪切测试（Ciarletta 等人，2011 年；Davis 和 De Vita，2014 年）[3, 4]，以及 9 种不同纤维角度的剪切计算（Horgan 和 Murphy，2017 年）[5]。由于考虑的情况多种多样，我们根据以下因素制定了具体的识别策略：1) 模型材料参数的线性或非线性特性；2) 通过谱方法对自由边界条件进行建模。