We present for the first time the feasibility to recover the stiffness (here shear modulus) distribution of a three-dimensional heterogeneous sample using measured surface displacements and inverse algorithms without making any assumptions about local homogeneities and the stiffness distribution. We simulate experiments to create measured displacements and augment them with noise, significantly higher than anticipated measurement noise. We also test two-dimensional problems in plane strain with multiple stiff inclusions. Our inverse strategy recovers the shear modulus values in the inclusions and background well, and reveals the shape of the inclusion clearly.
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The authors would like to acknowledge funding from the National Science Foundation under Grant No. CMMI #1663435 and thank for their support. The authors would also like to thank the High Performance Research Computing at Texas A&M University for their computing resources.
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Luo, P., Mei, Y., Kotecha, M. et al. Characterization of the stiffness distribution in two and three dimensions using boundary deformations: a preliminary study. MRS Communications 8, 893–902 (2018). https://doi.org/10.1557/mrc.2018.98