Identification of Gurson's material constants by using Kalman filter

A new approach based on the inverse analysis is proposed for estimating material parameters of nonlinear constitutive equations. Using the measurable response of experimental specimens, an inverse analysis is carried out to predict most suitable values of unknown material constants. In general, the accuracy of prediction depends on geometries of specimens and types of measurements. In order to identify optimal experimental procedure, the Kalman filter technique is employed. We have chosen the Gurson model for porous elastic-plastic materials as the material model and its two parameters as the unknown constants. Gurson's constitutive model has been widely used for studying ductile fracture as well as shear localization of various metals. Detailed finite element simulations are performed to demonstrate the effectiveness of the proposed method in determination of the two parameters relating to void nucleation. In the Kalman filter procedure, it is found that the rate of convergence to the correct solutions depends on shapes of test specimens, initial estimates of the unknown parameters, and accuracy of measured data as well as computed reference data. Our analysis predicts that when two differently shaped specimens under tension are used (i.e., a plate with a center hole and another with double side notches), a significant improvement occurs in the rate of convergence.