Chapter 9 On the Boundary Conditions and Optimization Methods in Integrated Digital Image Correlation S.M. Kleinendorst, B.J. Verhaegh, J.P.M. Hoefnagels, A. Ruybalid, O. van der Sluis, and M.G.D. Geers Abstract In integrated digital image correlation (IDIC) methods attention must be paid to the influence of using a correct geometric and material model, but also to make the boundary conditions in the FE simulation match the real experiment. Another issue is the robustness and convergence of the IDIC algorithm itself, especially in cases when (FEM) simulations are slow. These two issues have been explored in this proceeding. The basis of the algorithm is the minimization of the residual. Different approaches for this minimization exist, of which a Gauss-Newton method is used most often. In this paper several other methods are presented as well and their performance is compared in terms of number of FE simulations needed, since this is the most time-consuming step in the iterative procedure. Beside method-specific recommendations, the main finding of this work is that, in practical use of IDIC, it is recommended to start using a very robust, but slow, derivative-free optimization method (e.g. Nelder-Mead) to determine the search direction and increasing the initial guess accuracy, while after some iterations, it is recommended to switch to a faster gradient-based method, e.g. (update-limited) Gauss-Newton. Keywords Integrated digital image correlation • Boundary conditions • Optimization methods • Gauss-Newton • Nelder-mead • Trust-region 9.1 Introduction Interfacial delamination is a key reliability challenge in composites and micro-electronic systems due to (high-density) integration of dissimilar materials. Predictive finite element models are used to minimize delamination failures during design, but require accurate interface models to capture (irreversible) crack initiation and propagation behavior observed in experiments. A generic inverse parameter identification methodology is needed to identify the interface behavior in their as-received state in the micro-electronics component, while it is subjected to realistic loading conditions, such as thermal loading. Recently, Integrated Global Digital Image Correlation (IDIC) was introduced, which correlates the image patterns by deforming the images using as few as kinematically-admissible ‘eigenmodes’ as there are material parameters [1] in the interface model [2], thereby greatly enhancing noise insensitivity and robustness [3]. The main challenge lies in that the interface mechanics only generates very subtle changes in the deformation field of the adjacent material layers, therefore, especially high accuracy and robustness in the simulated deformation field is needed, as well as fast convergence because (FEM) simulations including interface mechanics are notoriously slow. To obtain high displacement accuracy, besides an accurate geometric and material model, precise boundary conditions have often been overlooked. A study into precise boundary conditions for the case of interface mechanics simulations has recently been conducted, see Ref. [4]. Therefore, boundary conditions is not the topic of this proceeding. High robustness and fast convergence can be equally important, hence, these topics are explored here. The robustness and convergence is determined by the IDIC algorithm. This algorithm is based on the brightness conservation relation, or optical flow relation, which means that material points retain the same brightness upon deformation of the underlying sample. It is with this principle that the displacement field calculated by using the material model is used to back-transform the deformed image to the reference configuration. If the displacement field is calculated correctly, the reference image and the back-transformed image should overlap perfectly (in the absence of noise and algorithm-induced errors such as interpolation) and hence the difference between these two images, denoted by the residual, will decrease to zero. Therefore, the heart of the IDIC algorithm, as well as for other DIC algorithms, is the minimization of this residual. S.M. Kleinendorst • B.J. Verhaegh • J.P.M. Hoefnagels ( ) • A. Ruybalid • O. van der Sluis • M.G.D. Geers Department of Mechanical Engineering, Eindhoven University of Technology, Gemini-Zuid 4.122, 5600MB, Eindhoven, The Netherlands e-mail: j.p.m.hoefnagels@tue.nl © The Society for Experimental Mechanics, Inc. 2018 L. Lamberti et al. (eds.), Advancement of Optical Methods in Experimental Mechanics, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-63028-1_9 55
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