A generalized orthotropic hyperelastic material model with application to incompressible shells (Q2712684)

The main feature of this report is a strain energy function modelling the finite deformation of orthotropic materials. This strain energy function is additionally composed of structural tensors which are products of unit vectors along principal material directions and three arbitrary tensor functions of right Cauchy-Green tensor. By virtue of the latter, the strain energy function is suitable for the description of different nonlinear properties in principal material directions. For practical purposes, the tensor functions are expanded in tensor power series. The strain energy function is simplified in the case when the principal strain axes coincide with principal material directions. In the case of infinitesimal strain, the St.-Venant-Kirchhoff model is recovered, and Valanis-Landel model and Ogden model are recovered in the case of isotropy. Using tests of the abdominal aorta of rats, which can be considered incompressible, the author determines 21 material parameters. Calculations with these parameters exhibit very good agreement with experiments within a considerable range of deformation. Then the author derives stress-deformation relations and tangent moduli. Finally, the resultrs are specialized to two-dimensional structures as sheets and membranes, and three problems are treated numerically. The results reported constitute an important contribution to nonlinear elasticity.