Contribution of heterogeneous strain field measurements and boundary conditions modelling in inverse identification of material parameters

Abstract

The present paper aims at applying the Finite Element Updating inverse method to several sample geometries by the means of Digital Image Correlation. The full-field data are experimentally obtained from three geometries exhibiting increasing strain fields heterogeneities. For each test, a Finite Element model is built and boundary conditions are duplicated from the measured displacements at the sample borders. Field comparisons are performed at several time steps until fracture occurs and a Levenberg-Marquardt method is used to solve the optimization problem. Six parameters of an anisotropic elastic-plastic constitutive model are identified and validated through the simulation of a deep-drawing forming operation. Results show that identification quality is improved when heterogeneous strain fields are used.

Identification of material parameters for thin sheets from single biaxial tensile test using a sequential inverse identification strategy

“…This procedure allows addressing the parameter identification problem using autonomous cost functions for each step, which are evaluated one after the other in a pre-specified sequence, as an alternative to perform the parameter identification by minimising a single cost function comprising all material parameters and results of different types, as commonly performed by other authors (e.g., [21,23,24,29]). As it will be shown in the next chapter, the use of a single cost function can lead to a somewhat inadequate description of the plastic behaviour of the material, namely the work-hardening.…”

“…In general, none constitutive model and identification strategy allows to perfectly describe the behaviour of a material. Finally, the use of deep-drawing tests for assessing the performance of the identification (e.g., [21,24,35,37,38]) is sensitive not only to the constitutive parameters but also to process parameters.…”

“…The non-linear nature of the plastic behaviour of metal sheets makes their characterisation quite complex, depending on factors such as: (i) the constitutive model used to describe the material hardening and anisotropic behaviour; (ii) the experimental tests, comprising the sample geometries and testing conditions and (iii) the strategy for identification of the constitutive parameters. Until now, there is no standard approach for performing the constitutive parameters identification, although several models for describing the yielding [1][2][3][4][5][6][7][8][9] and hardening [10][11][12][13][14][15][16] behaviours, and identification strategies [17][18][19][20][21][22][23][24][25][26] have been suggested. The use of deep-drawn components with increasingly elaborate geometries, together with the emergence of new metals and alloys in the sheet metal forming industry, has stimulated the development of sophisticated constitutive models, whose increased flexibility for describing the material plastic behaviour is associated with a larger number of parameters to identify.…”

Potential of the Cross Biaxial Test for Anisotropy Characterization Based on Heterogeneous Strain Field

“…In our case, it is very difficult to calculate precisely the relative displacements since a slight out of synchronization can lead to a small time lag between the two axes and the start of loading is not exactly the same for all the material points. Another approach [50] consists in prescribing the measured boundary conditions to the finite element model and use relative displacement to formulate the cost-function and thus cancel the influence of RBM. In this work, displacement fields are sufficiently unnoised to allow a proper strain calculation and thus define a stable cost-function.…”

Improving full-field identification using progressive model enrichments

“…Model Updating (FEMU [10,11,12,13,14,15]). In FEMU the gap between the experiment and simulations of the same experiment is minimized by optimizing 25 (i.e.…”