Convexity, polyconvexity and finite element implementation of a four-fiber anisotropic hyperelastic strain energy density—Application to the modeling of femoral, popliteal and tibial arteries

Cai, Renye; Hu, L.B.; Holweck, Frédéric; Peyraut, François; Feng, Zhi-Qiang

doi:10.1016/j.cma.2022.115294

Cited by 3 publications

(1 citation statement)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Kakavas et al present a mixed finite element formulation for approximating the large deformations observed in the analysis of elastomeric butt-joints [24]. In our previous work, considering the incompressibility of the material, we introduced a penalty function, and it has been successfully demonstrated that the finite element implementation of the polynomial strain energy function (SEF) constructed with this set of polyconvex invariants has been successfully executed within the FER University code [25]. So, the main purpose of this article is to broaden the application scope of these polyconvex invariants to model the behaviors of carbon fiber-woven materials.…”

Section: Introductionmentioning

confidence: 99%

Anisotropic Hyperelastic Strain Energy Function for Carbon Fiber Woven Fabrics

Cai,

Zhang,

Lai

et al. 2024

Materials

Self Cite

View full text Add to dashboard Cite

The present paper introduces an innovative strain energy function (SEF) for incompressible anisotropic fiber-reinforced materials. This SEF is specifically designed to understand the mechanical behavior of carbon fiber-woven fabric. The considered model combines polyconvex invariants forming an integrity basisin polynomial form, which is inspired by the application of Noether’s theorem. A single solution can be obtained during the identification because of the relationship between the SEF we have constructed and the material parameters, which are linearly dependent. The six material parameters were precisely determined through a comparison between the closed-form solutions from our model and the corresponding tensile experimental data with different stretching ratios, with determination coefficients consistently reaching a remarkable value of 0.99. When considering only uniaxial tensile tests, our model can be simplified from a quadratic polynomial to a linear polynomial, thereby reducing the number of material parameters required from six to four, while the fidelity of the model’s predictive accuracy remains unaltered. The comparison between the results of numerical calculations and experiments proves the efficiency and accuracy of the method.

show abstract

Section: Introductionmentioning

confidence: 99%