Inverse problem of breaking line identification by shape optimization

Abstract

AbstractAn inverse breaking line identification problem formulated as an optimal control problem with a suitable PDE constraint is studied. The constraint is a boundary value problem describing the anti-plane equilibrium of an elastic body with a stress-free breaking line under the action of a traction force at the boundary. The behavior of the displacement is observed on a subset of the boundary, and the optimal breaking line is identified by minimizing the {L^{2}}-distance between the displacement and the observation. Then the optimal control problem is solved by shape optimization techniques via a Lagrangian approach. Several numerical experiments are carried out to show its performance in diverse situations.