Higher-order elastic constitutive relation: Micro mechanism and application to acoustoelasticity

Abstract

Higher-order elastic constitutive relation is an important theoretical basis for acoustoelastic theory. However, the relation is usually established based on the macro mechanics, which is not suitable for revealing the micro mechanism at the atomic-scale. In this study, the elastic constitutive relation is reestablished based on the anharmonic interatomic forces and microscopic finite strain. The explicit expressions of nth-order elastic constants are obtained based on the Taylor expansion method. Besides, an acoustoelastic constitutive model is derived based on the second-order elastic constitutive relation. The acoustoelastic constitutive model shows that the velocity variation of wave propagation in pre-deformed crystals can be characterized by elastic constants. After that, the second-order elastic constitutive relation of four typical single crystals (iron, gold, silver and aluminum) is studied based on the molecular dynamics (MD). The calculated elastic constants are in good agreement with the previous results. In addition, single crystals gold and aluminum are used as examples, the acoustoelastic effect of the longitudinal wave is calculated based on the obtained elastic constants and simulated based on the MD. The calculated acoustoelastic effect is the same as the simulated one. The above results demonstrate that the anharmonic interatomic potential is the essential reason for the higher-order elastic constitutive relation and acoustoelastic effect.