A new hyperelastic strain energy function and integrity basis of invariants for modelling transversely isotropic materials

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:229

Article

Cai, Renye¹  Holweck, Frederic²  Feng, Zhi-Qiang^3,4  Peyraut, Francois² 

[1] Guangdong Polytech Normal Univ, Sch Automobile & Transportat Engn, Guangzhou, Guangdong, Peoples R China

[2] Univ Bourgogne Franche Comte, UTBM, ICB, CNRS,UMR 6303, F-90010 Belfort, France

[3] Southwest Jiaotong Univ, Sch Mech & Engn, Chengdu, Peoples R China

[4] Univ Paris Saclay, LMEE Univ Evry, F-91020 Evry, France

关键词: Strain Energy Function (SEF);    Biological soft tissue;    Polyconvexity;    Large deformation;    Nonlinear calculation;    Transversely isotropic hyperelastic materials;   

DOI  :  10.1016/j.ijsolstr.2021.111133

来源: Elsevier

【 摘 要 】

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. (c) 2021 Elsevier Ltd. All rights reserved.

【 授权许可】

Free