Noninvasive multilevel geometric regularization of mesh‐based three‐dimensional shape measurement

Abstract

Summary Finite element stereo digital image correlation (FE‐SDIC) requires a crucial calibration phase in which the initial CAD needs to be updated to fit the actual shape of the specimen. On the one hand, the use of a FE mesh facilitates the coupling of measurements with simulation tools, while on the other hand, it provides a unique, fine description of both the geometry and the displacement, which often makes the shape measurement problem highly ill‐posed. As a remedy, we propose a hybrid isogeometric‐FE strategy that can measure a shape in terms of spline functions while considering as an input and output the analysis‐suitable FE mesh. Making use of the appealing spline refinement procedures and of Bézier‐based operators, multilevel smooth spline discretizations are built concurrently with the initial FE subspace and related to the multiscale images used for the initialization of the shape measurement. It results in a geometrically sound regularization which provides a spline parametrization of the optimal shape along with its FE twin. A noninvasive implementation from an existing FE‐SDIC code is also detailed. The performance of the proposed method is assessed on real images and comparisons are made with other published techniques to prove its efficiency.

Free-Form Deformation Digital Image Correlation (FFD-DIC): A non-invasive spline regularization for arbitrary finite element measurements

“…The associated method can be classified as 2D-DIC (or simply DIC) [44,70,69,26,20,77], stereo-DIC [71,23,15,56,2] and Digital Volume Correlation (DVC) [4,41,24], respectively. In the case of stereo-DIC, a similar set up allows to measure the shape of a 3D mechanical surface [5,16,56,13], which is actually a fundamental step prior to any experiment for 3D surface displacement field measurements. The general DIC approach finds numerous applications in engineering: material characterization, geometry control, defect identification, model validation, etc.…”

“…When directly used to describe the kinematic measured field in DIC, they usually lead to ill-posed problems since the meshes contain too many degrees of freedom (dof) to optimize compared to the data provided by the experimental instrumentation (camera resolution, speckle pattern resolution, etc). Such a problematic is even more exacerbated in case of mesh-based shape measurement since the shape of the specimen is generally rather smooth and regular, and thus should require less dof than the corresponding simulated displacement field which may comprise important gradients [13]. To tackle this issue in FE-DIC, the common practice consists in resorting to what is referred to as the Tikhonov regularization technique in the field, i.e.…”

“…to add a specific term to the initial DIC objective function that penalizes the L 2 -norm of the gradient of each component of the measured field [50,56,16]. Yet, this treatment may create important artefacts, especially when the kinematic transformation involves global rotations [13].…”

“…As a result, besides the effort to implement spline functions in the DIC framework, the user ends up with an experimental displacement field that is not directly comparable with the output provided by most of today's simulation tools, which was the core interest of global approaches in DIC. An attempt to keep fields defined on FE meshes while taking advantage of the increased smoothness of B-Spline and NURBS functions has more recently been performed for shape measurements in [13]. The purpose was to make use of the explicit (Bézier-based) link from Lagrange nodal polynomials to spline functions [9,66,73] to project the initial FE shape measurement problem onto a smoother spline one.…”

“…Furthermore, the method is non-invasive with respect to a standard FE code (classic quadrature rules, element connectivities, etc). The strategy can ultimately be interpreted as a projection on a reduced, smooth basis and actually consists in a generalization of the technique introduced in [13].…”