The Reciprocity Gap Functional for Identifying Defects and Cracks

Huy Duong Bui (1) , Andrei Constantinescu (1) , Hubert Maigre (1)

1 LMS - Laboratoire de mécanique des solides

The recovery of defects and cracks in solids using overdetermined boundary data, both the Dirichlet and the Neumann types, is considered in this paper. A review of the method for solving these inverse problems is given, focusing particularly on linearized inverse problems. It is shown how the reciprocity gap functional can solve nonlinear inverse problems involving identification of cracks and distributed defects in bounded solids. Exact solutions for planar cracks in 3D solids are given for static elasticity, heat diffusion and transient acoustics.

Domaines: Mécanique [physics.med-ph]

Huy Duong Bui, Andrei Constantinescu, Hubert Maigre. The Reciprocity Gap Functional for Identifying Defects and Cracks. Zenon Mróz; Georgios Stavroulakis. Parameter Identification of materials and structures, 469, Springer-Verlag, pp.17-54, 2005, CISM International Centre for Mechanical Sciences, 9783211381342. ⟨10.1007/3-211-38134-1_2⟩. ⟨hal-00112504⟩