Analysis of Landau–Lifshitz and neo-Hookean models for static and dynamic acoustoelastic testing

Melnikov, Andrey and Malcolm, Alison and Poduska, Kristin M. (2022) Analysis of Landau–Lifshitz and neo-Hookean models for static and dynamic acoustoelastic testing. Physica Scripta, 97. ISSN 1402-4896

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Abstract

Acomparison of three different isotropic non-linear elasticmodels uncovers subtle but important differences in the acoustoelastic responses of amaterial slab that is subjected to dynamic deformations during a pump-probe experiment.The probewave deformations are small and are superimposed on larger underlying deformations using three differentmodels: Landau–Lifshitz (using its fourth-order extension), compressible neo-Hookeanmodel (properly accounting for volumetric deformations), and an alternative neo-Hookeanmodel (fully decoupled energies due to distortional isochoric and volumetric deformations). The analyses yield elasticity tensors and respective expressions for the propagation speeds of P-wave and S-wave probes for eachmodel.Despite havingmany similarities, the different models give different predictions ofwhich probe wave typeswill have speeds that are perturbed by differentpumpwave types. The analyses also showa conceptual inconsistency in the Landau–Lifshitzmodel, that a simple shear deformation induces a stress and a shear wave probe speed that depend on the second-order elastic constantλ, which controls resistance to volumetric changes and thus should not be present in the expressions for shear stress and shear wave probe speeds. Thus, even though the Landau–Lifshitz model is widely used, itmay not always be the best option to model experimental data.

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