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We present explicit reconstruction algorithms for fully anisotropic unknownelasticity tensors from knowledge of a finite number of internal displacementfields, with applications to transient elastography. Under certainrank-maximality assumptions satified by the strain fields, explicit algebraicreconstruction formulas are provided. A discussion ensues on how to fulfillthese assumptions, describing the range of validity of the approach. We alsoshow how the general method can be applied to more specific cases such as thetransversely isotropic one.

Reconstruction of a fully anisotropic elasticity tensor from knowledge of displacement fields