Nonlinear continuum mechanics of thick hyperelastic sandwich beams using various shear deformable beam theories

Abstract

In this study, the time-dependent mechanics of multilayered thick hyperelastic beams are investigated for the first time using five different types of shear deformation models for modelling the beam (i.e. the Euler–Bernoulli, Timoshenko, third-order, trigonometric and exponential shear deformable models), together with the von Kármán geometrical nonlinearity and Mooney–Rivlin hyperelastic strain energy density. The laminated hyperelastic beam is assumed to be resting on a nonlinear foundation and undergoing a time-dependent external force. The coupled highly nonlinear hyperelastic equations of motion are obtained by considering the longitudinal, transverse and rotation motions and are solved using a dynamic equilibrium technique. Both the linear and nonlinear time-dependent mechanics of the structure are analysed for clamped–clamped and pinned–pinned boundaries, and the impact of considering the shear effect using different shear deformation theories is discussed in detail. The influence of layering, each layer’s thickness, hyperelastic material positioning and many other parameters on the nonlinear frequency response is analysed, and it is shown that the resonance position, maximum amplitude, coupled motion and natural frequencies vary significantly for various hyperelastic and layer properties. The results of this study should be useful when studying layered soft structures, such as multilayer plastic packaging and laminated tubes, as well as modelling layered soft tissues.

A review on the nonlinear dynamics of hyperelastic structures

“…Layered hyperelastic structures have many applications in packaging industry (especially food packaging) [116][117][118][119], which makes it important to comprehend the behaviour of layered hyperelastic structures made of different materials. For this reason, Khaniki et al [120] examined five different shear deformable beam theories together with the Mooney-Rivlin strain energy model for analysing the nonlinear dynamics of sandwich soft beams. It was shown that considering the shear effect, layering and material positioning can highly affect the nonlinear resonance behaviour of the thick sandwich soft beam.…”