Influence of local cubic anisotropy on the transition towards an equipartition regime in a 3D texture-less random elastic medium - Archive ouverte HAL Access content directly
Journal Articles Wave Motion Year : 2020

Influence of local cubic anisotropy on the transition towards an equipartition regime in a 3D texture-less random elastic medium

Abstract

At long lapse times in randomly fluctuating media with macroscopic isotropy (texture-less media), the energy of elastic waves is equipartitioned between compressional (P) and shear (S) waves. This property is independent of the local isotropy or anisotropy of the heterogeneous constitutive tensor and of the type of source. However the local symmetry of the constitutive tensor does influence the rate of convergence to equipartition and this paper discusses the precise influence of local anisotropy on the time required to reach equipartition. More particularly, a randomly-fluctuating medium is considered, whose behavior is statistically isotropic, and locally cubic. After calculating all the differential and total scattering cross-sections in that case, an analytical formula is derived for the rate of convergence to the equipartition regime, function of the second-order statistics of the mechanical parameter fields (bulk and shear moduli and anisotropy parameter). The local anisotropy is shown to influence strongly that transition rate, with a faster transition when the fluctuations of the anisotropy parameter are positively correlated to those of the shear modulus. A numerical model is constructed to illustrate numerically these results. Since the asymptotic regime of equipartition cannot be simulated directly because it would require too large a computational domain, boundaries are introduced and mechanical properties are chosen so as to minimize their influence on equipartition.
Fichier principal
Vignette du fichier
Khazaie2019.pdf (2.15 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-02566857 , version 1 (07-05-2020)

Identifiers

Cite

Shahram Khazaie, Régis Cottereau. Influence of local cubic anisotropy on the transition towards an equipartition regime in a 3D texture-less random elastic medium. Wave Motion, 2020, 96, pp.102574. ⟨10.1016/j.wavemoti.2020.102574⟩. ⟨hal-02566857⟩
39 View
42 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More