Identification of Sheet Metal Constitutive Parameters Using Metamodeling of the Biaxial Tensile Test on a Cruciform Specimen

An identification strategy based on a machine learning approach is proposed to identify the constitutive parameters of metal sheets. The main novelty lies in the use of Gaussian Process Regression with the objective of identifying the constitutive parameters of metal sheets from the biaxial tensile test results on a cruciform specimen. The metamodel is intended to identify the constitutive parameters of the work hardening law and yield criterion. The metamodel used as input data the forces along both arms of the cruciform specimen and the strains measured for a given set of points. The identification strategy was tested for a wide range of virtual materials, and it was concluded that the strategy is able to identify the constitutive parameter with a relative error below to 1%. Afterwards, an uncertainty analysis is conducted by introducing noise to the force and strain measurements. The optimal strategy is able to identify the constitutive parameters with errors inferior to 6% in the description of the hardening, anisotropy coefficients and yield stresses in the presence of noise. The study emphasizes that the main strength of the proposed strategy relies on the judicious selection of critical areas for strain measurement, thereby increasing the accuracy and reliability of the identification process.