zbMATH — the first resource for mathematics

Invariant formulation of hyperelastic transverse isotropy based on polyconvex free energy functions. (English) Zbl 1033.74005
The paper presents a formulation of phenomenological strain energies for anisotropic hyperelastic materials at finite strain. The authors are interested in generating polyconvex strain energies. The anisotropy classes considered are transverse isotropy and orthotropy. The authors focus their attention on consititutive issues rather than on existence theorems, and therefore there is no discussion on the necessary growth conditions to ensure the existence; see [J. M. Ball, Arch. Ration. Mech. Anal. 63, 337–403 (1977; Zbl 0368.73040)]. Some numerical examples are provided. Comparison with experimental data is missing.

74B20 Nonlinear elasticity
74E10 Anisotropy in solid mechanics
Full Text: DOI