60 S.M. Kleinendorst et al. log(ν/ν p ) log(E/E p ) −1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 0 10 20 30 40 50 60 # FE simulations Fig. 9.6 Number of iterations needed before convergence within a set accuracy limit is reached for the Nelder-Mead method for a range of initial guesses. On the x-axis the initial guess in Poisson ratio , relative to the reference value p, is plotted. On the y-axis the initial guess in Young’s modulus E, with respect to the reference value Ep 0 10 20 30 40 50 60 70 80 103 104 105 106 # FE Simulation convergence criterion Nelder−Mead Trust-Region Gauss-Newton Fig. 9.7 Convergence plot for all three tested methods 9.4 Conclusions In integrated digital image correlation 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, which has 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. The results presented show varying performance and robustness for different methods. Derivative free methods, like Nelder-Mead, tend to require a great amount of iterations, but it should be noted that this may not be bad for performance, because perturbation of input parameters is not required and hence less FE evaluations, the most computationally expensive step, are executed per iteration. The custom Gauss-Newton with update limit is a robust and performance-wise
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