Nonlinear material identification of heterogeneous isogeometric Kirchhoff-Love shells

TL;DR

This paper introduces a robust inverse methodology using isogeometric finite element analysis to accurately identify heterogeneous material distributions in nonlinear Kirchhoff-Love shells, even with noisy experimental data.

Contribution

It presents a novel inverse approach combining nonlinear hyperelastic shell modeling with flexible material discretization and local optimization, enabling precise reconstruction of complex material distributions.

Findings

High accuracy in material distribution reconstruction with sufficient data.

Robustness against noise up to 4% in simulated experiments.

Efficient handling of material discontinuities through adapted discretizations.

Abstract

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.