Bulk thermoelastic attenuation of composite materials


  • Bernard Budiansky,

  • Eric E. Sumner Jr.,

  • Richard J. O'Connell


A theoretical derivation is made for the effective, frequency-dependent thermoelastic bulk modulus inline image of an isotropic composite subjected to hydrostatic stress inline image producing volumetric strain inline image. No heat transfer is permitted to occur at the outer boundary of the composite, but as a consequence of differential heating, heat transfer among the constituents, and hence dissipation, occurs in the interior. Thus between the limits ω = 0 and ω = ∞K*(ω) is complex and the thermoelastic damping may be measured by QK−1 = Im (K*)/Re(K*). Parametric studies show the influence of various elastic and thermal properties on thermoelastic damping. Numerical calculations are made for a hypothetical lower mantle assemblage of stishovite and magnesiowüstite. The results show that thermoelastic dissipation in the lower mantle can account for the observed attenuation of the fundamental radial normal mode and can also provide interesting constraints on grain sizes.