Energy balance and fundamental relations in dynamic anisotropic poro-viscoelasticity

Abstract

An energy balance equation and fundamental relations are obtained for wave motion in anisotropic poro‐viscoelastic media. The balance of energy identifies the strain and kinetic energy densities, and the dissipated energy densities due to viscoelastic and viscodynamic effects. The relations allow the calculation of these energies in terms of the Umov‐Poynting vector and kinematic variables. The energy balance is obtained for time‐harmonic fields, while the following relations are valid for inhomogeneous body waves. (i) The magnitude of the phase velocity is equal to the projection of the energy velocity vector onto the propagation direction. (ii) The time‐average of the dissipated energy density is obtained from the projection of the average power‐flow vector onto the attenuation direction. (iii) The time‐average energy density (kinetic plus strain) is obtained from the projection of the average power‐flow vector onto the propagation direction. (iv) The strain energy equals the kinetic energy when the medium is lossless. These relations are shown to be valid for anisotropic poro‐viscoelasticity at all frequency ranges. An example of ultrasonic wave propagation in an orthorhombic medium (human femoral bone saturated with water) illustrates the theory. Measurable quantities, like the attenuation factor and the energy velocity, can easily be interpreted in terms of microstructural properties such as tortuosity and permeability.