PSI - Issue 37

J. Henriques et al. / Procedia Structural Integrity 37 (2022) 25–32 J. Henriques et al. / Structural Integrity Procedia 00 (2021) 000 – 000

29 5

Similarly, the variables F exp and F num represent the experimental and numerical load, respectively, for the analyzed stage. A flowchart describing the material parameters identification chain using FEMU is presented in Fig. 2. An initial set of parameters ( χ ) is given to the finite element model in order to start the iterative process of FEMU. The numerical results, which are interpolated from the FEA mesh to the DIC mesh in order to match numeral data locations and experimental data points, are required to make an evaluation of the cost function. The iterative process continues using an optimization method to generate the next set of material parameters until a minimum of the objective function is reached, and the parameters set ( χ ) stagnate. The optimization method used is the Nelder-Mead simplex method, which is a simple direct-search algorithm (Gao and Han, 2012). Here, a simplex is generated beginning with as much vertices as the number of variables plus one, then a sequence of transformations is made with the goal of minimizing the objective function value at its vertices (Oliveira et al., 2021).

Fig. 2. Flowchart describing the material parameters identification chain using FEMU.

3. Results 3.1. Convergence study for identified parameters

The linear elastic orthotropic constitutive parameters ( E R , E T , ν RT and G RT ) are identified, being the only variables in the optimization process. Moreover, the initial set of material parameters are considered reference values and the W F used is 10 -3 , which privileges both the strain and the force terms minimization, as presented in Table 2. The optimization algorithm used is the fminsearch function from the MATLAB software library (MATLAB, 2021). The summary of the final objective function, strain and force terms values, and the comparison between the experimental force measurement and the final numerical force, for the seven specimens, are described in Table 2. Additionally, the convergence study for all four material parameters identified ( E R , E T , ν RT and G RT ) throughout the identification method, for all specimens, is presented in Fig. 3.