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

TL;DR

This paper develops explicit algorithms to reconstruct fully anisotropic elasticity tensors from internal displacement data, with applications in elastography, under certain mathematical assumptions, and extends methods to special cases like transversely isotropic materials.

Contribution

It introduces explicit algebraic reconstruction formulas for anisotropic elasticity tensors from displacement fields, including conditions for their validity and extensions to specific anisotropic cases.

Findings

Reconstruction algorithms work under rank-maximality assumptions.

Explicit formulas are derived for general anisotropic tensors.

Method can be adapted to transversely isotropic cases.

Abstract

We present explicit reconstruction algorithms for fully anisotropic unknown elasticity tensors from knowledge of a finite number of internal displacement fields, with applications to transient elastography. Under certain rank-maximality assumptions satified by the strain fields, explicit algebraic reconstruction formulas are provided. A discussion ensues on how to fulfill these assumptions, describing the range of validity of the approach. We also show how the general method can be applied to more specific cases such as the transversely isotropic one.