Shape derivative of an energy error functional for voids detection from sub-Cauchy data

Abstract

We study a new framework for a geometric inverse problem in linear elasticity. This problem concerns the recovery of cavities from the knowledge of partially overdetermined boundary data. The boundary data available for the reconstruction are given by the displacement field and the normal component of the normal stress, whereas there is lack of information about the shear stress. We propose an identification method based on a Kohn-Vogelius error functional combined with the shape gradient method. We put special focus on the identification of cavities and prove uniqueness for the case of monotonous cavities.

Keywords

• Geometric inverse problem
• cavities identification
• linear elasticity
• partially overdetermined boundary data
• Kohn-Vogelius error functional
• shape gradient