Abstract
A theoretical model concerning the finite bending of a prismatic hyperelastic solid has been recently proposed. Such a model provides the 3D kinematics and the stress field, taking into account the anticlastic effects arising in the transverse cross sections also. That model has been used later to extend the Elastica in the framework of finite elasticity. In the present work, Finite Element (FE) analyses of some basic structural systems subjected to finite bending have been carried out and the results have been compared with those provided by the theoretical model performed previously. In the theoretical formulation, the governing equation is the nonlinear local relationship between the bending moment and the curvature of the longitudinal axis of the bent beam. Such a relation has been provided in dimensionless form as a function of the Mooney–Rivlin constitutive constants and two kinematic dimensionless parameters termed Eulerian slenderness and compactness index of the cross section. Such parameters take relevance as they are involved in the well-known Searle parameter for bent solids. Two significant study cases have been investigated in detail. The results point out that the theoretical model leads to reliable results provided that the Eulerian slenderness and the compactness index of the cross sections do not exceed fixed threshold values.
Highlights
The nonlinear bending theory of elastic bodies has attracted a lot of interest because of its relevance in many physical and engineering applications
The theoretical results in terms of displacements of the longitudinal axis, stretch and stress distributions within the cross sections are compared with the results provided by Finite Element (FE) simulations
In order to highlight the effect induced by loss of Eulerian slenderness on the reliability of the theoretical model, Figure 6 shows the increase of the gap between the principal stretches λ X provided by the theoretical formulation and the FE simulations for subcase A1 (b)
Summary
The nonlinear bending theory of elastic bodies has attracted a lot of interest because of its relevance in many physical and engineering applications. Linear elasticity cannot be used to properly assess the mechanical response of bodies that exhibit large displacements and/or strains, like, for example, tentacle action or hand closure in soft robots For these and other contexts the finite elasticity is much more appropriate than the linearized theory. The nonlinear relation between the bending moment and the curvature of the longitudinal axis is written in a dimensionless form, highlighting the relevance of the Eulerian slenderness together with a second dimensionless parameter, which stands for the compactness of the transverse cross sections. Such parameters are coupled into the well known.
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