Detection of weak defects in elastic bodies through small amplitude homogenization. http://dx.doi.org/10.1080/17415977.2010.550046

Abstract

This article is devoted to the detection of inclusions using a single boundary measurement obtained from quasi-static essays in linear elasticity. The idea is to minimize the misfit between the displacement field obtained on part of the boundary and the boundary data coming from solving the elasticity equations with a guess inclusion. The optimization algorithm comes from the work of Allaire and Gutierrez [G. Allaire and S. Gutierrez, Optimal design in small amplitude homogenization, Math. Model. Numer. Anal. 41(3) (2007), pp. 543–574]
and it is based on the assumption that the contrast on the values of the Lame elastic coefficients between the defect and the matrix is not very large. This approach is promising because it is well adapted to cases when the defect is caused, for example, by weak inhomogeneities during the fabrication process.
From the numerical examples we conclude that the method is quite robust under noisy measurements and errors in the characterization of the defect.