Finite Bending of Fiber-Reinforced Visco-Hyperelastic Material: Analytical Approach and FEM

Abstract

This paper presents a new anisotropic visco-hyperelastic constitutive model for finite bending of an incompressible rectangular elastomeric material. The proposed approach is based on the Mooney–Rivlin anisotropic strain energy function and non-linear visco-hyperelastic method. In this study, we aim to examine the mechanical response of a reinforced viscoelastic rectangular bar with a group of fibers under bending. Anisotropic materials are typically composed of one (or more) family of reinforcing fibers embedded within a soft matrix material. This operation may lead to an enhancement in the strength and stiffness of soft materials. In addition, a finite element simulation is carried out to validate the accuracy of the analytical solution. In this research, the well-known stress relaxation test, as well as the multi-step relaxation test, are examined both analytically and numerically. The results obtained from the analytical solution are found to be in good agreement with those from the finite element method. Therefore, it can be deduced that the proposed model is competent in describing the mechanical behavior of fiber-reinforced materials when subjected to finite bending deformations.

Keywords

• anisotropic visco-hyperelasticity
• fiber-reinforced materials
• constitutive model
• finite element analysis
• relaxation tests