Finite bending of hyperelastic beams with transverse isotropy generated by longitudinal porosity

The paper deals with the finite bending analysis of transversely isotropic hyperelastic slender beams made of a neo-Hookean material with longitudinal voids. The fully nonlinear behavior of the structures is presented in the framework of three-dimensional finite elasticity. A semi-inverse approach is used to describe the beam kinematics, which includes the anticlastic effect. The theoretical framework is developed in both Lagrangian and Eulerian reference systems. Explicit formulas are obtained for stretches and stresses, in a general framework valid for transversely isotropic beams. The effect of porosity on the Piola-Kirchhoff and Cauchy stress components is then discussed. The results are all obtained and validated analytically, and could be helpful to model structural systems in the fields of bioengineering and soft-robotics which exhibit both large displacements and deformations.