MR-u: Material Characterization Using 3D Displacement-Encoded Magnetic Resonance and the Virtual Fields Method.

Background: Experimental, fully three-dimensional mechanical characterization of opaque materials with arbitrary geometries undergoing finite deformations is generally challenging. Objective: We present a promising experimental method and processing pipeline for acquiring and processing full-field displacements and using them toward inverse characterization using the Virtual Fields Method (VFM), a combination we term MR-u. Methods: Silicone of varying crosslinker concentrations and geometries is used as the sample platform. Samples are stretched cyclically to finite deformations inside a 7T MRI machine. Synchronously, a custom MRI pulse sequence encodes the local displacement in the phase of the MR image. Numerical differentiation of phase maps yields strains. Results: We present a custom image processing scheme for this numerical differentiation of MRI phase-fields akin to convolution kernels, as well as considerations for gradient set calibration for data fidelity. Conclusions: The VFM is used to successfully determine hyperelastic material properties, and we establish best practice regarding virtual field selection via equalization. [ABSTRACT FROM AUTHOR]