Nonlinear material identification of heterogeneous isogeometric Kirchhoff-Love shells

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.

37 pages, 18 figures, 5 tables

References in corpus (4)

• A NURBS-based Inverse Analysis for Reconstruction of Nonlinear Deformations of Thin Shell Structures
• A new rotation-free isogeometric thin shell formulation and a corresponding continuity constraint for patch boundaries
• Mechanical identification of layer-specific properties of mouse carotid arteries using 3D-DIC and a hyperelastic anisotropic constitutive model
• A novel in vivo approach to assess strains of the human abdominal wall under known intraabdominal pressure

Cited by in corpus (3)

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• A new anisotropic bending model for nonlinear shells: Comparison with existing models and isogeometric finite element implementation
• Nonlinear elastodynamic material identification of heterogeneous isogeometric Bernoulli-Euler beams