Comparative analysis of nonlinear dynamic behaviors of hyperelastic curved structure modelled by different constitutive laws

Abstract

This work focuses on conducting numerical studies and comparisons on the nonlinear dynamic behaviors of hyperelastic curved structures subjected to external dynamic loadings. A numerical model of the hyperelastic structure is developed using the nonlinear finite element method, which considers both the geometric nonlinearity resulting from large deformations and the material nonlinearity due to hyperelasticity. Four commonly used hyperelastic constitutive laws, namely the Mooney-Rivlin model, the neo-Hookean model, the Yeoh model, and the Ogden model, are employed to describe the nonlinear stress-strain relationship of the hyperelastic material. The convergence performance of the numerical model with respect to grid element and time step is thoroughly examined through several numerical examples. Subsequently, based on the developed numerical model, the nonlinear dynamic behaviors of the hyperelastic curved structures excited by uniform pressure loadings with single and dual frequencies are studied and compared using various constitutive laws. The material constants used in these constitutive laws are estimated based on the well-known Treloar's test data on vulcanized rubber material. Additionally, comprehensive parametric analyses are conducted on the nonlinear dynamic behaviors of the hyperelastic structure simulated by different constitutive laws. The deformation evolution process, resonance curves, time-frequency analysis, bifurcation diagrams, and phase portraits are employed to demonstrate the similarities and differences in the nonlinear dynamic behaviors (i.e., super- and sub-harmonic resonance, internal resonance, chaotic motion and bifurcations) of the hyperelastic structure modeled by different constitutive laws.