Propagation of fundamental Lamb modes along the non-principal axes of strain-stiffened soft compressible plates: A numerical investigation

Abstract

This paper numerically investigates the propagation of elastic plate waves along the non-principal directions in a prestretched compressible material described by the Gent model of hyperelasticity. We formulate the elastic tensor and the underlying wave equations in the Lagrangian space by employing the theory of nonlinear elasticity together with the linearized incremental equations. An extension of the Semi-Analytical Finite Element (SAFE) method is discussed for computing the dispersion characteristics of the two fundamental guided wave modes. The predictive capabilities of the numerical framework are established using the previously published data for a weakly nonlinear as well as hyperelastic material models. Using the numerical framework, we then bring out the effects of applied prestretch, orientation of the propagation direction, and material parameters on the dispersion characteristics of the fundamental Lamb modes. A limiting case of the neo-Hookean material model is first considered for elucidating such implicit dependencies, which are further highlighted by considering the strain-stiffening effect captured through the Gent material model. Our results indicate the existence of a threshold prestretch for which the Gent-type material can encounter a snap-through instability; leading to the change in the dispersion characteristics of the fundamental symmetric Lamb mode.