Reciprocity principle for the detection of planar cracks in anisotropic elastic material

The functionality of elastic devices can be strongly reduced by cracks. Therefore, it is important to develop nondestructive techniques for testing whether cracks exist inside the device, and if they exist, what the position and size of these cracks are. In this paper, we focus on the inverse method of measurements of boundary data for anisotropic elastic fields under different loads in order to detect cracks. We draw on the paper of Andrieux et al (1999 Inverse Problems 15 59-65), where a reciprocity principle is used for the detection of plane cracks in isotropic linear elastic materials. Utilizing that the setup and significant parts of the analysis by Andrieux et al are formulated generally and remain valid in anisotropic materials, we generalize this method for two-and three-dimensional transversely anisotropic elastic devices and demonstrate it by numerical experiments. We start from a cracked domain and generate boundary data as artificial measurements by solving numerically a forward problem. The inverse computations show good agreement between the simulated crack and the original one.