  This work presents a Finite Element Model Updating inverse methodology for
reconstructing heterogeneous material distributions based on an efficient
isogeometric shell formulation. It uses nonlinear hyperelastic material models
suitable for describing incompressible material behavior as well as initially
curved shells. The material distribution is discretized by bilinear elements
such that the nodal values are the design variables to be identified.
Independent FE analysis and material discretization, as well as flexible
incorporation of experimental data, offer high robustness and control. Three
elementary test cases and one application example, which exhibit large
deformations and different challenges, are considered: uniaxial tension, pure
bending, sheet inflation, and abdominal wall pressurization. Experiment-like
results are generated from high-resolution simulations with the subsequent
addition of up to 4% noise. Local optimization based on the trust-region
approach is used. The results show that with a sufficient number of
experimental measurements, design variables and analysis elements, the
algorithm is capable to reconstruct material distributions with high precision
even in the presence of large noise. The proposed formulation is very general,
facilitating its extension to other material models, optimization algorithms
and meshing approaches. Adapted material discretizations allow for an efficient
and accurate reconstruction of material discontinuities by avoiding overfitting
due to superfluous design variables. For increased computational efficiency,
the analytical sensitivities and Jacobians are provided.
