A local algorithm for the determination of interior material parameters from a knowledge of elastic displacements

Abstract

A new method is presented for the local determination of material parameters of an isotropic, inhomogenous medium subject to time harmonic vibration. Given a knowledge of the displacements throughout the medium, a novel implementation of a variational formulation is used to determine the ratios λ/ρ and μ/ρ. A theoretical formulation is presented and validated using numerical data obtained from a finite-element method. The results indicate that the method may be applied locally within an inhomogenous medium, and that the corresponding material parameters can be recovered to a high degree of accuracy. Because the method assumes knowledge of the displacements throughout the medium, various approaches to obtaining this information will also be discussed. [This work supported by the Office of Naval Research.]