In this paper we discuss the inverse problem of the identification of mechanical stresses by measuring the deformation of an electric potential field in a so called differential strain gauge (D-DMS). We derive a mathematical model, where the forward operator is given in terms of an elliptic boundary value problem. Derivatives of the forward operator are considered and the solution of the inverse problem via a least-squares minimization is introduced. Here, the discretized problem is solved with the Gauss-Newton method. Numerical studies of practical interest are presented.

In this paper we discuss the inverse problem of the identification of mechanical stresses by measuring the deformation of an electric potential field in a so called differential strain gauge (D-DMS). We derive a mathematical model, where the forward operator is given in terms of an elliptic boundary value problem. Derivatives of the forward operator are considered and the solution of the inverse problem via a least-squares minimization is introduced. Here, the discretized problem is solved with the Gauss-Newton method. Numerical studies of practical interest are presented.