Identification of Gurson-Tvergaard material model parameters via Kalman filtering technique. I. Theory

In this paper quasi-static ductile fracture processes are simulated within the framework of the finite element method by means of the Gurson-Tvergaard isotropic constitutive model for progressively cavitating elastoplastic so lids. The progressive degradation of the material strength properties in th e fracture process zone due to micro-void growth to coalescence is modeled through the computational cell concept. Among the several model parameters to be calibrated in the computations, attention is restricted to the Tverga ard coefficients q(1) and q(2) and to the initial porosity f(0) in the unst ressed configuration. To identify these model parameters the inverse proble m is solved via the extended Kalman filter for nonlinear systems coupled to a numerical methodology for the sensitivity analysis. In part I of this wo rk the theory of Kalman filtering and sensitivity analysis is presented. Fi rst results concerning the identification of the Tvergaard parameters for a whole crack growth in single edge notched bend specimens made of a pressur e vessel steel are presented. In order to enhance the convergence towards t he final solution of the identification procedure, during the tests measure ments are made of the displacements of points located in the central portio n of the notched specimens, where model parameters highly affect the system state variables. In part II of this work a numerical Validation of the pro posed procedure in terms of uniqueness of the final identified solution, re quirements of accuracy for the Bayesian initialization of the model paramet ers and sensitivity to the experimental measurement errors will be presente d and discussed.