Propagation of Polarization in Elastodynamics with Residual Stress and Travel Times

TL;DR

This paper demonstrates how the Dirichlet-to-Neumann map in elastodynamics can be used to determine wave travel times and residual stress, aiding inverse problems in material characterization.

Contribution

It establishes a method to recover residual stress and elastic parameters from boundary measurements in elastodynamics with residual stress.

Findings

Determined lens relations of pressure and shear waves from DN map.

Derived implications for inverse problems in elastodynamics.

Provided a framework for identifying residual stress and Lamé parameters.

Abstract

We show that knowing the Dirichlet-to-Neumann map (DN) associated to the equations of elastodynamics with residual stress we can determine the lens relations of presssure and shear waves. We derive several consequences of this for the inverse problem of determining the residual stress and the Lam\'e parameters from the DN map.