Numerical-empirical-based function for the assessment of the stiffness distribution on automotive body panels

The research presented in this paper deals with the development of a numerical-empirical-based model for the estimation of the indentation stiffness of automotive body panels, implemented in a self-developed simulation program for the quick and precise evaluation of the denting performances of newly developed parts during the design stage. The stiffness of the panels is estimated by calculating the major and minor curvatures, and their relevant variations, and can be applied also in the early stages of the design process, with no need for numerical simulations of the forming process required for the manufacturing of the panels. The model has been developed on the basis of a large number of indentation experiments carried out on existing automotive body panels (fender, front door, rear door, roof and hood) belonging to four different vehicle models. From the experiments, the load-stroke curve has been compared with the reference one (provided by the panels manufacturer) and the ratio between the integral area of the relevant experiment, and that of the reference curve has been defined as the stiffness index (SI). For all the tested specimens, between 18 and 24 points have been tested by means of indentation test whereas additional 20 points have been tested by means of numerical simulations, implemented in ABAQUS/Standard, in order to add additional data for the definition of the empirical model. The implemented numerical model has been initially validated by comparison its results with those of the laboratory experiments, showing a maximum error equal to 10.8%. Moreover, in order to account for the oil canning phenomenon (local softening), a penalization factor has been introduced in the model and has the effect of reducing the local SI values for the considered point of the panel. The regression model for the SI function has been calculated by utilizing the commercial software MINITAB with a correlation factor (R2) higher than 92%. Finally, the developed model has been implemented in a self-developed simulation program which allows imputing the CAD file of the panel and, within few minutes, to estimate the SI distribution on the part on the basis of the local curvatures (major and minor) and on the curvature variation calculated on the whole model.