Genetic Algorithm-Based Optimization Methodology of Bézier Curves to Generate a DCI Microscale-Model

The aim of this article is to develop a methodology that is capable of generating micro-scale models of Ductile Cast Irons, which have the particular characteristic to preserve the smoothness of the graphite nodules contours that are lost by discretization errors when the contours are extracted using image processing. The proposed methodology uses image processing to extract the graphite nodule contours and a genetic algorithm-based optimization strategy to select the optimal degree of the Bézier curve that best approximate each graphite nodule contour. To validate the proposed methodology, a Finite Element Analysis (FEA) was carried out using models that were obtained through three methods: (a) using a fixed Bézier degree for all of the graphite nodule contours, (b) the present methodology, and (c) using a commercial software. The results were compared using the relative error of the equivalent stresses computed by the FEA, where the proposed methodology results were used as a reference. The present paper does not have the aim to define which models are the correct and which are not. However, in this paper, it has been shown that the errors generated in the discretization process should not be ignored when developing geometric models since they can produce relative errors of up to 35.9% when an estimation of the mechanical behavior is carried out.