An adaptive procedure for defect identification problems in elasticity

In the context of inverse problems in mechanics, it is well known that the most typical situation is that neither the interior nor all the boundary is available to obtain data to detect the presence of inclusions or defects. We propose here an adaptive method that uses loads and measures of displacements only on part of the surface of the body, to detect defects in the interior of an elastic body. The method is based on Small Amplitude Homogenization, that is, we work under the assumption that the contrast on the values of the Lamé elastic coefficients between the defect and the matrix is not very large. The idea is that given the data for one loading state and one location of the displacement sensors, we use an optimization method to obtain a guess for the location of the inclusion and then, using this guess, we adapt the position of the sensors and the loading zone, hoping to refine the current guess.Numerical results show that the method is quite efficient in some cases, using in those cases no more than three loading positions and three different positions of the sensors.