Identification of Gurson's material constants by using Kalman filter

Abstract

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 ®lter 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 ®nite 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 ®lter 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 signi®cant improvement occurs in the rate of convergence.

Experimental determination of the void volume fraction for S235JR steel at failure in the range of high stress triaxialities

“…The obtained results are also higher than those reported in many studies concerning the GTN material model, i.e. f F = 0.15-0.25 [8,[12][13][14]. Another issue is the relationship between the critical void volume fraction f F and the prevailing stress intensity.…”

“…Its value differs depending on the material structure and the state of stress. Generally, f F is determined by combining experimental and numerical methods [11][12][13][14][15]; the other GTN parameters are defined in a similar way [3,[16][17][18].…”

An effective computational tool for parametric studies and identification problems in materials mechanics

“…This is done with specific reference to loadingunloading cycles of simple components, having in mind common experimental setting for material calibration purposes [20,21,[38][39][40][41][42]. However, the outcome of the present study can be easily generalised to many other meaningful engineering situations requiring to perform repetitive non-linear analyses of solids and structures.…”

“…Lagrange interpolation is then introduced in order to generalize the results to different input sets. The expected correlation of the system response permits to obtain a fairly accurate output with relatively low polynomial order (cubic and above, see e.g., [20][21][22][23][24]). Nonetheless, the number of direct analyses to be performed increases rapidly with the number of unknowns and with the selected polynomial order.…”

“…In a frequently adopted methodology, based on a proposal by Aoki et al [20], the system response is evaluated by the FE method in an a priori established number of parameter combinations, defining a regular grid of knot points in the sought parameter space. Lagrange interpolation is then introduced in order to generalize the results to different input sets.…”