Speaker
Description
The heterogeneity of natural materials is inherent and poses significant challenges in determining their mechanical properties, such as stiffness and density. Since biological samples are often very fragile, special care is necessary to examine them with traditional material testing. Moreover, applying the standard methods might be impossible in in-vivo conditions. These issues cause increasing interest in non-destructive methods, including inverse approaches based on full-field experimental data. This study employs the Finite Element Model Updating (FEMU) method for material identification of heterogeneous Kirchhoff-Love shells and planar Bernoulli-Euler beams, which are analyzed numerically with isogeometric analysis. The unknown material fields are discretized with a separate mesh based on Lagrange interpolation, referred to as the material mesh. The nodal values of the material mesh become discrete unknowns of the inverse problem. The framework focuses on reconstructing stiffness parameters through inverse analysis based on nonlinear statics, followed by identifying density unknowns using modal dynamics. The FEMU objective function is formulated as a least-squares problem, mainly consisting of the differences between experimental and FE displacements. The objective function may also include, for instance, resultants of the contact forces or natural frequencies, depending on the underlying FE problem. Quasi-experimental data is artificially generated using high-resolution FE models with random noise added subsequently. To solve the nonlinear least-squares problem, the Trust Region Interior Reflective algorithm is used. Furthermore, analytical gradients and Jacobians are derived and implemented to accelerate the computations. The FEMU approach is tested with several numerical examples, including a shell strip subjected to uniform pressure and an abdominal wall under rigid contact with a spherical probe. Results show that the approach is sensitive to noise. However, with sufficient experimental data, i.e., higher resolution of experimental mesh or the number of experiments involved, the influence of noise can be significantly reduced. The method enables the identification of smooth and discontinuous distributions, even for large noise levels. Additionally, the density can be accurately reconstructed based on the previously obtained stiffness. The analytical sensitivities provide a huge decrease in the computational time required for the inverse analysis. The material mesh can act as a filter to prevent overfitting. Its adaptivity is crucial and will be explored in future research.
