Shape features and finite element model updating from full-field strain data

Finite element model updating is an inverse problem based on measured structural outputs, in this case maximum principal strain measured using digital image correlation. Full-field responses in the form of strain maps contain valuable information for model updating but within large volumes of highly-redundant data. In this paper, shape descriptors based on Zernike polynomials having the properties of orthogonality and rotational invariance are shown to be powerful decomposition kernels for defining the shape or map of the strain distribution. A square plate with a circular hole subject to a uniaxial tensile load is considered and effective shape features are constructed using a set of modified Zernike polynomials. The modification includes the application of a decaying weighting function to the Zernike polynomials so that high strain magnitudes around the hole are well-represented. The Gram–Schmidt process is then used to ensure orthogonality for the obtained decomposition kernels over the domain of the specimen, i.e. excluding the hole. Results show that only a very small number of Zernike moment descriptors are necessary and sufficient to represent the full-field data. The onset of yielding may be quantified using the descriptors. Furthermore, model updating of nonlinear elasto-plastic material properties is carried out using the Zernike moment descriptors derived from full-field strain measurements.