Finite Element Stereo Digital Image Correlation: Framework and Mechanical Regularization

Abstract

The use of Finite Element meshes in Digital Image Correlation (FE-DIC) is now widespread in experimental mechanics. Up to now FE have been much less used in Stereo-DIC. The first goal of this paper is to explain in details how to use FE in Stereo-DIC using a formulation in the physical coordinate system. More precisely, it is shown how to perform the calibration of possibly nonlinear models, shape and displacement measurement based on a FE mesh. In addition it is shown that with such a framework it is possible to regularise the measurement with a FE model based on the same mesh. For instance, using this technique, it is shown that it is possible to measure the rotation field of a bending plate in addition to its displacement.

A Space-Time PGD-DIC Algorithm:

“…In this section, particular care is taken to provide a global formalism that is suitable for both standard Finite Element Digital Image Correlation (FE-DIC [35,7]) and the newly developed Finite Element Stereo Digital Image Correlation (FE-SDIC [13,28,33]). …”

“…-SDIC allows the three components of the displacement in Ω s to be measured when using a larger number of inclined cameras n c > 1. In this case, u denotes a three-component displacement field [28].…”

“…A dedicated quadrature rule was proposed in [29] and further enhanced in [28] for multiple camera and/or non-linear camera models.…”

“…Here, we propose to use a Finite Element based Digital Image Correlation (FE-DIC) method. The recent developments in the field of FE-DIC [35,7] and the even more recent advances in Finite Element Stereo DIC (FE-SDIC) [13,29,28,33] allow a direct link with the simulation tools. It is thus possible to share the same FE mesh during the calculation and the measurement, in the aim of (a) greatly simplifying the bridge between simulation and experimentation, and (b) limiting the uncertainties associated with reprojection.…”

“…In this paper we propose to prescribe time-smoothness as a physical regularization technique in the space domain. This technique should not be opposed to existing space regularization methods [20,30,31,28,11,33], but should be rather seen as an additional tool, which can positively complement more conventional remedies. More precisely, the method starts from a space-time formulation of DIC [6,8].…”