MCRE-based parameter identification from full-field measurements: Consistent framework, integrated version, and extension to nonlinear material behaviors

Abstract

In this paper, we address the effective and robust identification of material behavior parameters from full-field measurements obtained by means of the advanced Digital Image Correlation (DIC) experimental technique. The objective is to optimize the identification procedure by defining an appropriate and flexible numerical methodology that automatically incorporates the limited knowledge on both the used mathematical model (which is always biased, whatever its complexity) and experimental data (which are numerous in the case of DIC, but inevitably noisy). The inverse methodology we propose, denoted DIC-mCRE, is based on the modified Constitutive Relation Error (mCRE) concept which is a convenient tool to deal with reliability of information. In this framework, the designed identification tool is constructed from a hybrid mathematical formulation with a cost function made of weighted modeling and observation error terms. The associated metric thus naturally considers and connects all error and uncertainty sources. We introduce here a consistent setting of the weighting factors with respect to measurement noise, that gives full sense to the quantification of the model quality. Additionally, an integrated version (called mI-DIC) of the methodology is developed, and an extension to nonlinear constitutive models is proposed together with a dedicated solver. The performance of the approach is analyzed and validated on several numerical experiments dealing with linear elasticity or nonlinear models, and using synthetic or real full-field data.