A Novel Algorithm for Optimal Discretization of Stress–Strain Material Curves for Application in Finite Element Analyses

Abstract

The maximal vertical distance (MVD) recursive algorithm, a novel approach for the optimal discretization of stress–strain material curves, is proposed. The algorithm simplifies the process of defining multilinear curves from material stress–strain curves when conducting a finite element analysis (FEA) of components. By directly selecting points on the material curve, the MVD algorithm eliminates the requirement for initial discretization, thereby minimizing information loss. As the measure of goodness of fit of the simplified polyline to the original curve, the percentage of stress deviation (SD) is proposed. The algorithm can generate multiple multilinear curves while keeping the stress deviation of each curve within a predefined limit. This feature is particularly beneficial during the finite element analysis of components exhibiting complex and position-dependent material properties, such as surface-hardened components, ensuring consistent modelling accuracy of material properties across the components’ geometry. Consistent accuracy also proves advantageous when exploring multiple differing material states of quenched and tempered steel, ensuring fair and reliable comparisons. The MVD algorithm was compared with existing algorithms from the literature, consistently maintaining the accuracy of the multilinear curves within predetermined limits using the fewest possible points.

Keywords

• stress–strain curve
• finite element analysis
• multilinear material model
• optimization algorithm
• optimal discretization