Large deformation analysis of fully incompressible hyperelastic curve d b eams

The aim of this contribution is to develop a nonlinear formulation for modelling the large deformation of elastic curved beams made of fully incompressible hyperelastic materials. The basic idea is to apply the incompressibility constraint besides the plane stress assumption in the directions perpendicular to the centreline of the beam. Accordingly, a system of three nonlinear algebraic equations for the hydrostatic pressure as well as normal strain components in the beam cross section are obtained. By solving the system of equations, either analytically or numerically, it is possible to propose constitutive equations for the force and moment resultants present in the formulation. The main advantage of this strategy is that it allows for using three-dimensional incompressible constitutive equations. Due to highly nonlinear nature of the differential equations, a Total Lagrangian finite element formulation is developed. Performance and accuracy of the formulation are investigated through several numerical examples. (c) 2020 Elsevier Inc. All rights reserved.

Automated summary

This contribution presents a nonlinear formulation for modeling the large deformation of elastic curved beams made of fully incompressible hyperelastic materials. By applying an incompressibility constraint and a plane stress assumption, a system of three nonlinear algebraic equations involving hydrostatic pressure and normal strain in the beam cross section is obtained. This strategy allows for using three-dimensional incompressible constitutive equations and a Total Lagrangian finite element formulation due to the highly nonlinear nature of the differential equations. Performance and accuracy of the formulation are examined through numerical examples.