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.