  Contemporary material characterisation techniques that leverage deformation
fields and the weak form of the equilibrium equations face challenges in the
numerical solution procedure of the inverse characterisation problem. As
material models and descriptions differ, so too must the approaches for
identifying parameters and their corresponding mechanisms. The widely-used
Ogden material model can be comprised of a chosen number of terms of the same
mathematical form, which presents challenges of parsimonious representation,
interpretability, and stability. Robust techniques for system identification of
any material model are important to assess and improve experimental design, in
addition to their centrality to forward computations. Using fully 3D
displacement fields acquired in silicone elastomers with our recently-developed
magnetic resonance cartography (MR-u) technique on the order of $>20,000$
points per sample, we leverage PDE-constrained optimisation as the basis of
variational system identification of our material parameters. We incorporate
the statistical F-test to maintain parsimony of representation. Using a new,
local deformation decomposition locally into mixtures of biaxial and uniaxial
tensile states, we evaluate experiments based on an analytical sensitivity
metric, and discuss the implications for experimental design.
