Detecting Rigid Inclusions, or Cavities, in an Elastic Body

In this paper we address the following problem of nondestructing testing: to determine, within an elastic body , the possible presence of defects in the form of either cavities or rigid inclusions, from measurements of traction and displacement taken at the exterior boundary of . Let us denote by D the unknown, possibly disconnected, defect and let us assume that D is an open set compactly contained in and that \D is connected. Let the elasticity tensor C = C(x), x ∈ , be given at a reference configuration (i.e., without defects) of the elastic body. First, let us consider the case when D is a cavity. The displacement field uv in \D corresponding to assigned tractions φ applied on ∂ is given as the solution of the Neumann problem for the system of linearized elasticity  div (C∇uv) = 0 in \D, (C∇uv)ν = φ on ∂ , (C∇uv)ν = 0 on ∂D, (1.1)