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October 9, 2023
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Article

Bayesian inference of high-dimensional finite-strain visco-elastic–visco-plastic model parameters for additive manufactured polymers and neural network based material parameters generator

Publicated to:International Journal Of Solids And Structures. 283 112470- - 2023-11-01 283(), DOI: 10.1016/j.ijsolstr.2023.112470

Authors: Wu, L; Anglade, C; Cobian, L; Monclus, M; Segurado, J; Karayagiz, F; Freitas, U; Noels, L

Affiliations

Cirp GmbH - Author
Cirp GmbH, Romerstr 8, D-71296 Heimsheim, Germany - Author
IMDEA Mat Inst, Calle Eric Kandel 2, Getafe 28906, Madrid, Spain - Author
IMDEA Materials Institute - Author
IMDEA Materials Institute , Universidad Politécnica de Madrid - Author
Univ Liege, Dept Mech & Aerosp Engn Computat & Multiscale Mech, Allee Decouverte 9, B-4000 Liege, Belgium - Author
Univ Politecn Madrid, Dept Mat Sci, ETSI Caminos, Madrid 28040, Spain - Author
Universite de Liege - Author
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Abstract

In this work, the parameters of a finite-strain visco-elastic–visco-plastic formulation with pressure dependency in both the visco-elastic and visco-plastic parts are identified using as observations experimental data obtained from tension and compression tests at different strain rates ranging from 10−4s−1 to 103s−1. Because of the high number of parameters of the model, a sequential Bayesian Inference (SBI) framework with data augmentation, which presents several advantages, is developed. First the sequential nature reduces the difficulty of selecting the appropriate prior distributions by considering only parts of the observations at a time. Second, the sequential nature prevents dealing with low likelihood values by considering only a part of the experimental observations at a time, but also subsets of the material parameters to be identified, improving the convergence of the Markov Chain Monte Carlo (MCMC) random walk. Third, the data augmentation allows considering different number of experimental tests in tension and in compression while preserving the identified model accuracy for both loading modes. This SBI is carried out to infer the properties of Polyamide 12 (PA12) processed by Selective Laser Sintering (SLS) for two different printing directions and it is shown that the models fed by their respective set of inferred parameters can reproduce the different experimental tests. Finally, in order for upcoming structural simulations to benefit from the information related to the uncertainties due to the measurement errors, the identification process and the model limitations, we introduce a Generative Adversarial Network (GAN), which is trained using the data obtained from the MCMC random walk. This generator can then serve to produce a synthetic data-set of arbitrary size of the material parameters to be used in finite-element simulations.

Keywords

behaviorformulationgenerative adversarial networkhomogenizationidentificationmechanical-propertiespolyamideselective laser sinteringvisco-elasticity-visco-plasticityBayesian inferenceGenerative adversarial networkMicromechanical analysisPolyamideSelective laser sinteringVisco-elasticity–visco-plasticity

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal International Journal Of Solids And Structures due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2023, it was in position 39/170, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mechanics.

From a relative perspective, and based on the normalized impact indicator calculated from the Field Citation Ratio (FCR) of the Dimensions source, it yields a value of: 1.85, which indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: Dimensions Jul 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-07-18, the following number of citations:

  • WoS: 3
  • Scopus: 3

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-07-18:

  • The use, from an academic perspective evidenced by the Altmetric agency indicator referring to aggregations made by the personal bibliographic manager Mendeley, gives us a total of: 9.
  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 13 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

  • The Total Score from Altmetric: 1.
  • The number of mentions on the social network X (formerly Twitter): 1 (Altmetric).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Belgium; Germany.