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This work is devoted to the study of the void identification problem from partially overdetermined boundary data in the 2D-elastostatic case. In a first part, a shape identifiability result from a Cauchy data is presented, i.e. with traction field and boundary displacement as measurements. Then this geometric inverse problem is tackled by the minimization of two cost functionals, an energy gap functional and anL  2{L^{2}}   -gap functional, which enable the reconstruction of voids under Navier’s boundary conditions. The shape derivatives of these cost functionals are computed for the purpose of sensitivity analysis.

Shape sensitivity analysis for identification of voids under Navier’s boundary conditions in linear elasticity