Identification of elastic properties from full-field measurements: a numerical study of the effect of filtering on the identification results

Abstract

The use of full-field displacement measurements in mechanical testing has increased dramatically over the last two decades. This is a result of the very rich information they provide, which is enabling new possibilities for the characterization of material constitutive parameters for inhomogeneous tests often based upon inverse approaches. Nonetheless, the measurement errors limit the accuracy of the identification of the constitutive parameters and their possible spatial resolution. The question addressed by this work is the following: can a filtering of the displacement measurement improve the results of the identification of elastic properties? The discussion is based on the study of a numerical example where the elastic parameters of an elastic structure with inhomogeneous properties are sought from synthetic data representative of in-plane full-field data. The displacement data are first filtered through a diffuse approximation algorithm, based on a moving least-squares approximation. Then, the identification of the elastic parameters is performed by an inverse approach based on the minimization of a cost function, defined as the least-squares gap between the experimental data and their numerical counterpart (finite element model updating). Within this framework, a first-order analysis is proposed in order to characterize the errors in the identified parameters, the measurement error characteristics being known. Results from raw and filtered displacement data are compared and discussed, filtering improving the identification for lower spatial resolution. The choice of the norm to define the gap between the experiment and the calculation is also discussed. For practical use and to take advantage of the proposed first-order methodology, two different ways can be considered: applying the methodology to a numerical example, representative of the experimental setup, to determine whether or not a filtering is valuable, and estimating the uncertainties of the identified parameters at the end of the identification process of an experimental characterization.

Multiscale Displacement Field Measurement Using Digital Image Correlation: Application to the Identification of Elastic Properties

“…Different optimization techniques, norms . and cost functions may be used to exploit measured displacement fields [21,8,6,22,11]. For instance, in [6,22] strain fields are compared.…”

“…For instance, in [6,22] strain fields are compared. In the following, we rather compare directly the displacement fields to avoid the amplification of the measurement noise linked to a numerical differentiation [11,56]. This calls for a strengthened emphasis on the boundary conditions.…”

“…[8] or [1] for more details. However a drawback of this approach is obviously that the level of uncertainty associated with the identified parameters depends on the quality of the kinematic measurements [11], and thus in our concern, of the DIC displacement measurement uncertainties [12]. The latter are related at least to the DIC method itself [13], but also depend strongly on the spatial resolution of the displacement measurement [14,13].…”

Identification of elastic properties in the belief function framework

“…There are two main challenges: (1) faithfully representing prior information, and (2) quantifying uncertainties from various sources and propagating them. Recently, a lot of methods have been proposed to identify material properties from kinematic fields, including Finite Element Model Updating (FEMU) [10,11,12], the Constitutive Relation Error Method (CREM) [13,14], the Modified Constitutive Relation Error Method (M-CREM) [15], the Equilibrium Gap Method (EGM) [16,17,18], and the Virtual Fields Method (VFM) [19,20]. These methods do not specifically address the issues of exploiting prior information and quantifying uncertainty.…”