Sensitivity analysis of the of the square cup stamping process using a polynomial chaos expansion

Abstract. The stochastic modelling and quantification of the various sources of uncertainty associated with sheet metal forming processes, usually requires a large computational cost to obtain accurate results. In this work, a polynomial chaos expansion metamodel is used in order to reduce the computational cost of the uncertainty quantification (through Sobol’s indices). The metamodel allows to establish mathematical relationships between the square cup forming results and the uncertainty sources associated with the material behaviour and process conditions. Then, sensitivity indices are estimated with the trained metamodel, without resorting to additional numerical simulations. The indices obtained with the metamodel were compared to those obtained with the traditional approach based on a quasi-Monte Carlo method. The metamodel allowed to reduce the computational cost in about 90% when compared to the traditional approach, without compromising the accuracy of the results.