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 solids. The progressive degradation of the material strength properties in the 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 Tvergaard coefficients q(1) and q(2) and to the initial porosity f(0) in the unstressed configuration. To identify these model parameters the inverse problem is solved via the extended Kalman filter for nonlinear systems coupled to a numerical methodology for the sensitivity analysis. In part I of this work the theory of Kalman filtering and sensitivity analysis is presented. First results concerning the identification of the Tvergaard parameters for a whole crack growth in single edge notched bend specimens made of a pressure vessel steel are presented. In order to enhance the convergence towards the final solution of the identification procedure, during the tests measurements are made of the displacements of points located in the central portion of the notched specimens, where model parameters highly affect the system state variables. In part II of this work a numerical Validation of the proposed procedure in terms of uniqueness of the final identified solution, requirements of accuracy for the Bayesian initialization of the model parameters and sensitivity to the experimental measurement errors will be presented and discussed.