Uniqueness in the inverse boundary value problem for piecewise homogeneous anisotropic elasticity

Cătălin I. Cârstea, Gen Nakamura

Published 2016-11-12Version 1

Consider a three dimensional piecewise homogeneous anisotropic elastic medium $\Omega$ which consists of a finite number of bounded Lipschitz domains $D_\alpha$, with each $D_\alpha$ a homogeneous elastic medium. One typical example is a finite element model for an ansiotropic elastic medium. Assuming we know the boundary of each $D_\alpha$, we are concerned with the uniqueness in the inverse boundary value problem of identifying the anisotropic elasticity tensor on $\Omega$ from a localized Dirichlet to Neumann map given on a part of the boundary $\partial D_{\alpha_0}\subset\partial\Omega$ of $D_{\alpha_0}$ for a single $\alpha_0$. If we can connect each $D_\alpha$ to $D_{\alpha_0}$ by a chain of $\{D_{\alpha_i}\}_{i=1}^n$ such that interfaces between adjacent regions contain a curved portion, we obtain global uniqueness for this inverse boundary value problem.