Bending of hyperelastic beams made of transversely isotropic material in finite elasticity

The paper aims to investigate the finite bending of hyperelastic beams composed of transversely isotropic soft materials. The constitutive laws are obtained by including the transverse isotropy effects in the compressible Mooney-Rivlin model. A suitable expression for the stored energy function is introduced for this purpose, showing its dependency on five material invariants. A fully nonlinear three-dimensional beam model, including the anticlastic effect, is developed. The general analytical formulation allows to consider the influence of transverse isotropy on the Piola-Kirchhoff and Cauchy stress components, since it is presented in both Lagrangian and Eulerian frameworks. The validity of the current model is finally discussed. This study is justified by many innovative applications which require the use of transversely isotropic components, such as the finite bending of soft robots or biological systems