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.

本文研究了一种新的具有纵向空隙的霍克材料制成的横观各向同性超弹性细长梁的有限弯曲分析。在三维有限弹性的框架内呈现了结构的完全非线性行为。半逆方法用于描述梁的运动学，其中包括抗扭效应。理论框架在拉格朗日参考系统和欧拉参考系统中都得到了发展。在对横观各向同性梁有效的通用框架中，获得了拉伸和应力的显式公式。然后讨论了孔隙度对Piola-Kirchhoff和Cauchy应力分量的影响。所有结果均已获得并经过分析验证，