Accuracy of the Neo-Hookean material models in the analysis of longitudinal-vibration problems

• Investigate effect of the shear modulus in neo-Hookean material (NHM) models in longitudinal-vibration problems. • Use ANCF elements with general NHM models to develop new benchmark problems with different boundary conditions. • New models with different boundary conditions demonstrate NHM stiff behavior compared to the analytical solution. • It is shown that the shear-energy term can absorb 50% of the total strain energy in longitudinal-vibration problems. Nonlinear n eo- H ookean m aterial (NHM) models are written in terms of two Lame’s constants; one of them is the shear modulus. The NHM strain-energy term that depends on the shear modulus does not approach zero as the shear strain approaches zero. This paper demonstrates the effect of this strain-energy term in longitudinal-vibration problems, characterized by zero shear and transverse-normal strains at the integration points. To this end, fully parameterized finite-element (FE) beam models with complete sets of gradient vectors are used to allow implementing general NHM models. In developing such models, distinction is made between constraint-free end conditions (CFEC) and stress-free end conditions (SFEC). The latter requires enforcing natural boundary conditions , which are not required for the CFEC models. The results show that the NHM model leads to stiff behavior and oscillation frequencies that are different from the analytical solution. It is shown that the strain-energy term that depends on the shear modulus can absorb approximately 50% of the total strain energy in longitudinal-vibration problems.