Geodesics: a tool for solving material properties inverse problems

摘要

Inverse problems in mechanics of solids and structures are gaining more importance. One of the reason behind that is the advances in digital image processing and computer vision technologies. Traditionally, the user would locate features on the object or attach grids to it. The deformation of those features (or grids) would give an indication of the displacements undergone by some points on the surface of the object due to the deforming forces. Knowledge of the deforming forces and the displacements is usually enough to approximate the material properties of the object. In this paper we suggest a method by which a featureless object can be interrogated for its material properties. No invasive procedures are necessary. The method uses geodesics of the deformed and undeformed surfaces to obtain the displacements due to known deforming forces. Finite element method is then used to deduce the material properties distribution of the object. The method is proven to work only for elastic deformations that would leave a deformed surface developable with respect to the undeformed one.