Ogden Material Calibration via Magnetic Resonance Cartography, Parameter Sensitivity, and Variational System Identification

Abstract

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.

arXiv comment19 pages, 8 figures

References in corpus (9)

• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Data-driven computational mechanics
• Unsupervised discovery of interpretable hyperelastic constitutive laws
• Automated derivation of the adjoint of high-level transient finite element programs
• Discovery of Nonlinear Multiscale Systems: Sampling Strategies and Embeddings
• Data driven problems in elasticity
• Variational system identification of the partial differential equations governing pattern-forming physics: Inference under varying fidelity and noise
• Machine learning materials physics: Multi-resolution neural networks learn the free energy and nonlinear elastic response of evolving microstructures
• Variational system identification of the partial differential equations governing microstructure evolution in materials: Inference over sparse and spatially unrelated data

Cited by in corpus (2)

• Modelling brain tissue elasticity with the Ogden model and an alternative family of constitutive models
• Parsimonious inertial cavitation rheometry via bubble collapse time