Wave equations in linear viscoelastic materials.
Conditions for writing wave equations in linear viscoelastic materials are investigated. The study is restricted to the infinitesimal theory and an application is suggested in modeling ultrasound propagation in soft biological tissues. First, a general wave equation is obtained for the displacement field in an inhomogeneous medium. Second, the propagation of "the mean principal stress" (i.e., minus the arithmetical mean of the principal stresses) is examined. That quantity is particularly relevant when the force per unit area is detected at the surface of a nondissipative coupling medium. If the material is homogeneous, a wave equation is always obtained for the mean principal stress. Otherwise, supplementary conditions have to be assumed on the material and possibly on the motion. Results are illustrated by examples which present linearly elastic perfect fluids and linearly elastic Newtonian viscous fluids as particular viscoelastic materials.
D000005:Abdomen / Q000473:pathology; D000162:Acoustics; D004548:Elasticity; D006801:Humans; D008433:Mathematics; D014463:Ultrasonography / Q000379:methods*; D014783:Viscosity