This chapter presents a new inverse analysis method of finding local elastic moduli from displacement data for a heterogeneous and anisotropic elastic body in state of plane stress or strain. The method chooses a small block by connecting points at which displacement is measured and analyzes its deformation to determine elastic moduli separately from the rest of the body. The procedures of the elasticity inversion are developed with some techniques to exclude measurement errors from the displacement data. It is demonstrated in numerical simulation that the elasticity inversion is able to determine local elastic moduli accurately, when displacement data of sufficient quantity and quality is given. The limitations in applying the elasticity inversion: (1) only relative values are found, (2) discretization errors cannot be fully removed from data, and (3) the prediction becomes less accurate as less smooth displacement fields are used.
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