Kube Christopher M, Norris Andrew N
Weapons & Materials Research Directorate, U.S. Army Research Laboratory, Building 4600, Aberdeen Proving Ground, Maryland 21005-5069, USA.
Mechanical and Aerospace Engineering, Rutgers University, Piscataway, New Jersey 08854, USA.
J Acoust Soc Am. 2017 Apr;141(4):2633. doi: 10.1121/1.4979980.
A lower bound to the longitudinal and shear attenuation ratio was recently derived for viscoelastic materials [Norris, J. Acoust. Soc. Am. 141, 475-479 (2017)]. This letter provides proof that a similar bound is present for low-frequency attenuation constants of polycrystals caused by grain scattering. An additional upper bound to the attenuation ratio is unveiled. Both bounds are proven to be combinations of wave speeds. The upper and lower bounds correspond with the vanishing of the second-order anisotropy of the bulk and shear modulus, respectively. A link to the polycrystalline Poisson's ratio is highlighted, which completely bounds the attenuation ratio. An analysis of 2176 crystalline materials was conducted to further verify the bounds.
