A manifold learning-based reduced order model for springback shape characterization and optimization in sheet metal forming

Quilliec, Guénhaël Le; Raghavan, Balaji; Breitkopf, Piotr

doi:10.1016/j.cma.2014.11.029

Cited by 26 publications

(11 citation statements)

References 39 publications

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“…However, this would demand extensive off-line simulations in most cases simply to construct with sufficient accuracy a global manifold for identification, since it is always high-dimensional and nonlinear. In the present work, we propose an on-line approach which constructs only the useful portion of M (local manifold) progressively by using the predictor-corrector strategy issued from our former work [38,39]. Thus the manifold is represented by a series of local polynomials.…”

Section: Algorithm Familiesmentioning

confidence: 99%

“…In the present work, we propose a novel material parameter identification protocol based only on the imprint shape of the indentation test using Proper Orthogonal Decomposition [33,34] and manifold learning [35][36][37]. Following [38,39], originally applied to the numerical assessment of spring back for the deep drawing process, we build a "shape space" [40] and we apply the concept of shape manifold to describe all the imprint shapes admissible for a postulated constitutive law. The shape manifold is constructed by a series of simulated shape imprints using Design of Experiments (DOE) and POD approach.…”

Section: Introductionmentioning

confidence: 99%

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Identification of material properties using indentation test and shape manifold learning approach

Liang

Breitkopf

Raghavan

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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The conventional approach for the identification of the work hardening properties of a material by an indentation test usually relies on the force-displacement curve. However, finite element modeling of the indenter-specimen system is a complex task, and the unicity of the solution to the inverse problem of identifying material parameters using the force-displacement curve is not always guaranteed. Also, the precise measurement of the displacement of the indenter tip requires the determination of the indenter frame compliance and indenter tip deformation. To alleviate these problems, we propose in this work an approach based solely on the 3D indentation imprint shape measured after indenter withdrawal, rather than relying on the minimization of the pointwise discrepancy between the experimental and simulated indentation curve. We first build a mathematical "shape space" of indentation shapes in which a lower-dimensional manifold of imprints admissible according to a postulated material constitutive law is approximated. Then, we solve the inverse problem by using a series of predictor-corrector algorithms minimizing the distance between the estimated solution and the experimental imprint in this shape space. We finally apply the proposed approach to indentation tests using a spherical tip indenter on two different materials: a C100 steel specimen and a specimen of the AU4G (AA2017) aluminium alloy.

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Section: Algorithm Familiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Identification of material properties using indentation test and shape manifold learning approach

Liang

Breitkopf

Raghavan

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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“…Though supervised variants exist, the typical manifold learning problem is unsupervised: it learns the high-dimensional structure of the data from the data itself, without the use of predetermined classifications. Engineering applications include manufacturing processes (see [45], where a manifold walking algorithm is used, and [76]) and mechanical tests [56], and structural optimization problems [75]. Among other we mention its application in natural science, for instance [3].…”

Section: New Opportunities In Parameter Studies: Active Subspacesmentioning

confidence: 99%

Advances in Geometrical Parametrization and Reduced Order Models and Methods for Computational Fluid Dynamics Problems in Applied Sciences and Engineering: Overview and Perspectives

Salmoiraghi¹,

Ballarin²,

Corsi³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Several problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments.

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“…The shape b a c Fig. 2 Examples of products of varying shape complexity and compactness: a middle shape complexity, middle compactness, b high shape complexity, middle compactness, c low shape complexity, low compactness complexity and compactness are related to the number of types of faces, the different face orientations, the levels in the face hierarchy and many other geometric futures and can be formally defined [31]. In the presented research, it was assumed that due to the specifics of the method and the limited availability of the data under the RFQ conditions, the experts' intuitional assessment presented in the form of the linguistic values is sufficient.…”

Section: The Formulation Of a Numerical Examplementioning

confidence: 99%

Knowledge-based methods for cost estimation of metal casts

Macioł

2016

Int J Adv Manuf Technol

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The aim of the research presented in this paper was to verify the hypothesis that the problem of estimating the variable costs of metal casts can be solved by using knowledge-based systems. The estimation of variable costs determines the adequate pricing of products, which is a crucial marketing problem in enterprises. The problem of estimating the direct costs is especially important in companies whose participation in the market is defined as versatile manufacturing. This problem was the target of many studies presented in this paper. The assumptions that the direct costs of a metal cast are dependent on the physical features of the cast and the most effective method of cost estimation is an intuitive qualitative technique based on a rule-based system were considered. The nature of the relationships between the casts' features and the direct costs of production could be effectively formed by experts as reasoning rules. In this paper, the results of experiments conducted on the basis of the example of the production program of a foundry that manufactures water-system fittings is presented. Three methods of knowledge-definition and reasoning techniques were examined: the classical method of crisp reasoning, fuzzy reasoning with the Mamdani's method, and fuzzy reasoning with the Takagi-Sugeno model. Proper experiments were conducted. The results of the experiments confirmed the hypothesis, which allows the assessment of different reasoning methods.A. Maciol

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A manifold learning-based reduced order model for springback shape characterization and optimization in sheet metal forming

Cited by 26 publications

References 39 publications

Identification of material properties using indentation test and shape manifold learning approach

Identification of material properties using indentation test and shape manifold learning approach

Advances in Geometrical Parametrization and Reduced Order Models and Methods for Computational Fluid Dynamics Problems in Applied Sciences and Engineering: Overview and Perspectives

Knowledge-based methods for cost estimation of metal casts

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