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Finite Element Stereo Digital Image Correlation Measurement for Plate Model Jean-Emmanuel Pierre´, Jean-Charles Passieux, and Jean-Noe¨l Pe´rie´ Abstract The aim of this study is to measure accurately the boundary conditions, namely the displacements and rotations, along the edges of a large part of a composite panel subjected to complex loadings. With classical Stereo Digital Image Correlation techniques (Stereo DIC), the displacement field can only be measured on the upper skin. The rotations are usually estimated a posteriori by numerical differentiation and smoothing. Unfortunately additional uncertainties may arise with these steps. Conversely, the use of a Finite Element plate model is proposed here to regularize a Stereo Finite ElementDIC measurement (Stereo FE-DIC). The idea is to use the 3D displacement as the primary unknown of the correlation problem. This approach thus requires projection operators (here based on a pinhole camera model). It allows taking into account distortions directly. Keywords Stereovision • Digital Image Correlation • Mechanical regularization • Finite element • Distortion

25.1

Introduction

This study is part of a project (ANR VERTEX) that aims to perform tests on composite plates of dimensions 500
500 mm2 in order to validate damage models (Fig. 25.1). This sample size allows an original scale of structural details and allows treating fundamental problems. The drawback is that non-conventional testing resources in which instrumental ad hoc resources have to be used. In this project, it is for instance proposed to use stereo DIC to provide the boundary conditions needed by the partners in order to validate a damage model. For a plate model, boundary conditions are three displacements and two rotations. A stereo correlation method is more likely to measure the displacements of the upper skin, and the rotations are not directly estimated. The rotations can be obtained by a posteriori numerical differentiation. Since the measured displacement is noisy, smoothing techniques which usually do not consider the mechanical nature of the measured field are usually exploited. In this work, an integrated DIC approach is preferred. A plate finite element model is used to regularize a priori the stereo correlation measurement. A dedicated FE Stereo DIC method was developed accordingly. More precisely, Digital Image Correlation (DIC) [1–3] consists in measuring the displacement field u between two images, f and g in two different loading conditions (at t0 and t1). The displacement field measured on the images is assumed to correspond to the actual displacement of the object. Finite element interpolations have been proposed which allow bridging more efficiently numerical models and experiments [4–8]. Classically, the optical flow problem is written in a weak form over a region called Region of Interest (ROI) which is usually defined by a subset of the reference state image f (Eq. (25.1)). u⋆ ¼ argmin

ð

u2L ðROI Þ ROI

½ f ðxÞ  gðx þ uðxÞÞ2 dx

ð25:1Þ

2

For one increment of Stereo Correl