Calibration of Anisotropic Plasticity Models with an Optimized Heterogeneous Test and the Virtual Fields Method

Abstract

An accurate calibration of a constitutive model for finite element analysis is as important as an adequate choice of the constitutive model itself. The calibration strategy and the experimental database have determinant roles for the success of this stage. Over recent years, the increasing use of full-field measurement techniques has changed significantly the amount of data that compose the experimental database and suppressed some of the design constraints of the mechanical tests. These techniques enable to capture complete displacement/strain fields during a mechanical test, a feature that has been conveniently used to explore heterogeneous mechanical tests. The use of full-field measurements and heterogeneous tests has proven to be an interesting approach to calibrate complex models with a high number of material parameters, such as the case of anisotropic plasticity models. Usually, the inverse strategies selected to identify the material parameters from heterogeneous fields are based on the so-called finite element model updating (FEMU) method, which is known for being computationally demanding. Nevertheless, novel inverse strategies, such as the virtual fields method, have demonstrated much better results in terms of the computational cost without deterioration of the calibration results. Therefore, the aim of the present study, in the framework of full-field measurements, is to explore the combination of a previously designed heterogeneous test and the virtual fields method (VFM). The heterogeneous test consists of a uniaxial standard test with an optimized specimen shape, called butterfly shape. This specimen was specifically designed to obtain a wide range of strain paths and strain amplitudes and has given promising results when combined with a FEMU-based strategy. A set of virtual fields is developed to combine the butterfly test and the VFM. This set is tested with virtual experimental data generated and the sensitivity of the VFM to the number of virtual fields is confirmed. Moreover, experimentally acquired full-field measurements of butterfly test for a DC04 mild steel are used to assess the performance of this calibration strategy. An anisotropic plasticity model composed by Hill’48 and Swift’s law is calibrated.