Constitutive modeling of transversely isotropic materials to describe the mechanical behavior of thick-walled cylindrical tubes

There are different categories of materials like elastomers, polymers, hydrogel foams, and biological tissues that respond with large deformations (in comparison with solid metals) while under small stresses. By using a strain energy density function, it is possible to investigate their non-linear mechanical behavior. In the current study a strain energy density function for transversely hyperelastic material is proposed and its coefficients are approximated (using least square error) by incorporating experimental results into the model. Expected deviations between the proposed model and the experimental results for the fibrous layer of articular capsule, ligaments, and the human knee tendos are bounded by 1e-5 MPa and 1e-7 Mpa respectively. The proposed strain energy density function is a function of two invariants with more accuracy than the proposed one by Qiu and Pence, Merodio and Ogden and Guo et al. which uses a strain energy density function with only one invariant. Using the strain energy density function, a closed analytical form independent of integrals terms for expressing the stress within a thick-walled cylindrical tube for transversely isotropic hyperelastic materials, that has similar mechanical behavior to that of a human artery, is derived. The analysis for the stress, deformations is done considering artery like structures with both ends open and closed while under axial loads.