Modified constitutive relation error identification strategy for transient dynamics with corrupted data: The elastic case

Feissel, Pierre; Allix, Olivier

doi:10.1016/j.cma.2006.10.005

Cited by 69 publications

(100 citation statements)

References 10 publications

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“…A first reason is related to the measurement uncertainties and biases that are usually higher than those typically encountered in 2D analyses [23,24]. Second, the computational environment needed to solve these inverse problems is generally very intrusive (e.g., constitutive equation gap method [25][26][27], virtual fields method for nonlinear constitutive laws [28], equilibrium gap method [29]). Third, nonlinear constitutive equations require spatiotemporal (i.e., 4D) analyses to be considered, which are both experimentally and computationally very demanding.…”

Section: Introductionmentioning

confidence: 99%

Toward 4D mechanical correlation

Hild

Bouterf

Chamoin

et al. 2016

Adv. Model. and Simul. in Eng. Sci.

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Background: The goal of the present study is to illustrate the full integration of sensor and imaging data into numerical procedures for the purpose of identification of constitutive laws and their validation. The feasibility of such approaches is proven in the context of in situ tests monitored by tomography. The bridging tool consists of spatiotemporal (i.e., 4D) analyses with dedicated (integrated) correlation algorithms. Methods: A tensile test on nodular graphite cast iron sample is performed within a lab tomograph. The reconstructed volumes are registered via integrated digital volume correlation (DVC) that incorporates a finite element modeling of the test, thereby performing a mechanical integration in 4D registration of a series of 3D images. In the present case a non-intrusive procedure is developed in which the 4D sensitivity fields are obtained with a commercial finite element code, allowing for a large versatility in meshing and incorporation of complex constitutive laws. Convergence studies can thus be performed in which the quality of the discretization is controlled both for the simulation and the registration. Results: Incremental DVC analyses are carried out with the scans acquired during the in situ mechanical test. For DVC, the mesh size results from a compromise between measurement uncertainties and its spatial resolution. Conversely, a numerically good mesh may reveal too fine for the considered material microstructure. With the integrated framework proposed herein, 4D registrations can be performed and missing boundary conditions of the reference state as well as mechanical parameters of an elastoplastic constitutive law are determined in fair condition both for DVC and simulation.

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Section: Introductionmentioning

confidence: 99%

Toward 4D mechanical correlation

Hild

Bouterf

Chamoin

et al. 2016

Adv. Model. and Simul. in Eng. Sci.

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“…Another approach consists of applying level set methods to describe the shape of the sought cavity [4]. Instead of looking for the cavity's shape, it is also possible to try to directly identify Young's modulus spatial field within the studied domain, as it is applied in specific examples in [5,6] using a specific constitutive relation error in addition to the initial misfit function.…”

Section: Introductionmentioning

confidence: 99%

Using mesh adaption for the identification of a spatial field of material properties

Puel

Aubry

2011

Numerical Meth Engineering

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SUMMARYIt is well known that the solution of an inverse problem is ill-posed and not unique. To avoid difficulties caused by this, when solving such a problem, Tikhonov's regularization terms are usually added to the norm quantifying the discrepancy between the model's predictions and experimental data. This regularization term however is often inadequate to perform the identification of a field of material properties that varies spatially. This is all the more difficult when dealing with the numerical solution of this inverse problem, for the sought field is spatially discretized and this discretization can influence the result of the identification.We will here examine an overall strategy using classical adaptive meshing methods used to circumvent these drawbacks. The first step consists of using two distinct meshes: one associated with the discretization of the sought spatial field and the other associated with the solution of the mechanical problems (forward and adjoint states). In the second step, we will introduce local error estimators that allow an oriented refinement of the mesh associated with the sought parameters.This general strategy is applied to a practical case study: the detection of underground cavities using experimental data obtained by an interferometric device on a satellite. We will then address the question of how the regularization terms and the error estimator driving the mesh refinement were selected.

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“…An improvement could be achieved through the interpolation from separate coarse DIC solutions to fine boundary distributions for I-DIC. Another solution would be the introduction of the boundary conditions to the set of unknowns [65,66] in I-DIC approaches. In that case DIC analyses would not be required.…”

Section: Hardening Responsementioning

confidence: 99%