Finite Element Modeling of Ultrasonic Waves in Viscoelastic Media

Abstract

Linear viscoelasticity theory offers a minimal framework within which to construct a consistent, linear and causal model of mechanical wave dispersion. The term dispersion is used here to imply temporal wave spreading and amplitude reduction due to absorptive material properties rather than due to geometrical wave spreading. Numerical modeling of wave propagation in absorptive media has been the subject of recent research in such areas as material property measurement [1] [2], seismology [3] [4] [5] and medical ultrasound [6] [7]. Previously, wave attenuation has been included in transient finite element formulations via a constant damping matrix [8] or functionally in terms of a power law relation [9]. The formulation presented here is based on representing the viscoelastic shear and bulk moduli of the medium as either a discrete or continuous spectrum of decaying exponentials [10]. As a first test of the correctness of the viscoelastic finite element formulation, the finite element results for a simple hypothetical medium are compared with an equivalent Laplace-Hankel transform domain solution.