Accuracy of the Neo-Hookean material models in the analysis of longitudinal-vibration problems
Year: 2025
Type: article
Abstract: 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.
Source: Journal of Sound and Vibration
Author: Ahmed A. Shabana
Institution: University of Illinois Chicago
Language: English
Subfield: Biomedical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,190
OpenAlex ID: W4410090872