Adjusting fictitious domain parameters for fairly priced image-based modeling: Application to the regularization of Digital Image Correlation

Abstract

The integration of numerical simulation and experimental measurements in cellular materials at the sub-cellular scale is a real challenge. On the experimental side, the almost absence of texture makes displacement fields measurement tricky. On the simulation side, it requires the construction of reliable and specimen-specific geometric and mechanical models from digital images. For this purpose, high order based fictitious domain approaches have proven to be an efficient alternative to boundary conforming finite elements for the analysis of geometrically complex objects. A number of discretization parameters needs to be set by the user by making a trade-off between accuracy and computational cost. In addition to numerical errors (interpolation, integration etc.), there are additional geometric and model errors due to the pixelation of the image (e.g., quantization, sampling, noise). In the literature, discretization parameters are often analyzed without taking pixelation into account, which can lead to over-calculations. In this paper, these parameters are adjusted to obtain (a) the best possible accuracy (bounded by pixelation errors) while (b) ensuring minimal complexity (concept of fair price). In order to analyze the different sources of error, various two-dimensional synthetic experiments are generated by mimicking the image acquisition process from high-resolution numerical simulations considered as a reference. The approach leads to a modeling that outperforms conventional approaches both in terms of accuracy and complexity. Eventually, it is shown that the presented image-based models provide a unique opportunity to assist digital volume correlation and allow the measurement of relevant local kinematics within cellular materials.

Architecture-Driven Digital Image Correlation Technique (ADDICT) for the measurement of sub-cellular kinematic fields in speckle-free cellular materials

“…The proposed ADDICT draws on research dealing with FE-DIC [28,29,30,31,32], weak mechanical regularization [24,16,33,34], and immersed image-based modeling [8,35,9,23]. This section introduces the main ingredients of the method and accounts for the choices performed from the current technologies of the literature.…”

“…In this context, the basis functions defining V can be chosen, for example, as the standard nodal Lagrange polynomial functions [29,44,32], or more regular spline functions in the spirit of free-form deformation models [45,46,47] or isogeometric analysis [30,31,48,23].…”

“…The method relies on immersed B-spline image-based mechanical modeling for the automatic and accurate description of the local kinematic of the imaged sample without using the classical meshing procedures [23]. Then we make use of a tuned equilibrium gap method for the weak regularization of the DIC problem [24,25].…”

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

“…Formally, the FFD regularization can be seen as a discretization of a fictitious domain approach [65,74,60]. Consequently, it has similar problems to address, as the handling of conditioning problems caused by non-influential control points over the region of interest, which led us to the definition of a criterion to quantify the influence of a control variable.…”

“…T condition number as will be seen in section 4.5. For that reason, we decided to use a criterion on the influence of a control point (through its corresponding function) derived from criteria that are used by the fictitious domain community [65,74,60]. propose the following criterion for a control point P i :…”