The adjoint-weighted equation method for the direct solution of inverse problems of elasticity
Résumé
We apply the adjoint weighted equation method (AWE) for the direct solution of inverse problems of elasticity where the shear modulus distribution is reconstructed from given strain data. We demonstrate that while continuous and noise-free data provides accurate reconstructions, for discontinuous or noisy data the reconstruction is challenging. For those cases, we show that data smoothing and regularization of the solution offer a dramatic improvement. These are necessary when considering real-world measured strain data.
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