New Strain Energy Function for Acoustoelastic Analysis of Dilatational Waves in Nearly Incompressible, Hyper-Elastic Materials

Acoustoelastic analysis has usually been applied to compressible engineering materials. Many materials (e.g., rubber and biologic materials) are “nearly” incompressible and often assumed incompressible in their constitutive equations. These material models do not admit dilatational waves for acoustoelastic analysis. Other constitutive models (for these materials) admit compressibility but still do not model dilatational waves with fidelity (shown herein). In this article a new strain energy function is formulated to model dilatational wave propagation in nearly incompressible, isotropic materials. This strain energy function requires four material constants and is a function of Cauchy–Green deformation tensor invariants. This function and existing (compressible) strain energy functions are compared based upon their ability to predict dilatational wave propagation in uniaxially prestressed rubber. Results demonstrate deficiencies in existing functions and the usefulness of our new function for acoustoelastic applications. Our results also indicate that acoustoelastic analysis has great potential for the accurate prediction of active or residual stresses in nearly incompressible materials.