ANALYSIS OF LANDAU–LIFSHITZ AND NEO-HOOKEAN MODELS FOR STATIC AND DYNAMIC ACOUSTOELASTIC TESTING
Date
2022
Authors
Melnikov, Andrey
Malcolm, Alison E
Poduska, Kristin M
Journal Title
Journal ISSN
Volume Title
Publisher
Physica Scripta
Abstract
A comparison of three different isotropic non-linear elastic models uncovers subtle but important
differences in the acoustoelastic responses of a material slab that is subjected to dynamic deformations
during a pump-probe experiment. The probe wave deformations are small and are superimposed on larger
underlying deformations using three different models: Landau–Lifshitz (using itsfourth-order extension),
compressible neo-Hookean model(properly accountingfor volumetric deformations), and an alternative
neo-Hookeanmodel(fully decoupled energies due to distortional isochoric and volumetric deformations).
The analyses yield elasticity tensors and respective expressionsfor the propagation speeds of P-wave and
S-wave probesfor each model. Despite having many similarities, the different models give different
predictions of which probe wave types will have speeds that are perturbed by different pump wave types.
The analyses also show a conceptual inconsistency in the Landau–Lifshitz model, 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
expressionsfor shear stress and shear wave probe speeds. Thus, even though the Landau–Lifshitz model is
widely used, it may not always be the best option to model experimental data.
Description
Keywords
Type of access: Open Access, Landau–Lifshitz and neo-Hookean models
Citation
Melnikov, A., Malcolm, A., & Poduska, K. M. (2022). Analysis of Landau–Lifshitz and neo-Hookean models for static and dynamic acoustoelastic testing. Physica Scripta, 97(12), 125012. https://doi.org/10.1088/1402-4896/ac9be1