Special Issue "Constitutive Modelling for Metals"

A special issue of Metals (ISSN 2075-4701).

Deadline for manuscript submissions: 31 December 2018

Special Issue Editors

Guest Editor
Prof. Robertt Valente

Department of Mechanical Engineering, Universidade de Aveiro, Aveiro, Portugal
Website | E-Mail
Interests: finite element method (FEM) and isogeometric analysis (IgA); constitutive modelling; plastic forming; joining processes
Guest Editor
Prof. Myoung-Gyu Lee

Department of Materials Science and Engineering, Korea University, Seoul, Korea
Website | E-Mail
Interests: constitutive modelling for advanced structure materials; theory of plasticity; anisotropic plasticity; multi-scale computational modelling

Special Issue Information

Dear Colleagues,

In a world facing constant technological evolution, and where a circular economy represents the dominant paradigm, the optimized use of raw materials with the lowest energetic impact is a strong (and increasingly important) requirement. Together with this rational use of resources, structural requirements for final products are a key factor for materials science and mechanical engineers. To this aim, physically-consistent, reliable and computationally-efficient constitutive modelling is the cornerstone of an efficient design.

Within this Special Issue on "Constitutive Modelling for Metals", we aim to provide a wide visibility for the most up-to-date and relevant works in this field, from both experimental and modelling/numerical simulation standpoints.

Following your research achievements in the field of constitutive modelling, we would like to invite you and your group to submit a contribution to this Special Issue of Metals (http://www.mdpi.com/journal/metals). Being an open access journal with a high impact factor (http://www.mdpi.com/journal/metals/stats) we are sure your work will have a strong impact for a wide range of readers.

The deadline for papers submission is 31 of December, 2018. After receiving a submission, it will be processed following the review process. After the revision stages, accepted papers in their final form will be immediately published with a specific label mentioning the Special Issue, with no delay (i.e., with no need to wait for other papers in the Special Issue).

We hope you accept this invitation, and help us to make a high-impact and high-quality Special Issue on "Constitutive Modelling for Metals". In the case of a positive answer, please let us know as soon as possible so that we can inform the Editorial Office about your inclusion.


Prof. Robertt Valente
Prof. Myoung-Gyu Lee
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Metals is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


  • Anisotropic yield criteria
  • Anisotropic hardening
  • Computational constitutive modelling and experimental validation
  • Conventional and innovative numerical simulation techniques
  • Damage criterion and fracture propagation
  • Industrial applications (aeronautic, automotive, beverage cans, etc.)
  • Modelling of advanced joining technologies (FSW, SPR, mechanical joints, etc.)
  • Multi-scale computational models and their implementation
  • Springback, rupture and wrinkling predictions
  • Theoretical and numerical practice for novel forming technologies

Published Papers (1 paper)

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Open AccessArticle Quadratic Midpoint Integration Method for J2 Metal Plasticity
Metals 2018, 8(1), 66; doi:10.3390/met8010066
Received: 7 December 2017 / Revised: 11 January 2018 / Accepted: 16 January 2018 / Published: 18 January 2018
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The quadratic variants of the generalized midpoint rule and return map algorithm for the J2 von Mises metal plasticity model are examined for the accuracy of deviatoric stress integration of the constitutive equation. The accuracy of stress integration using a strain rate
[...] Read more.
The quadratic variants of the generalized midpoint rule and return map algorithm for the J2 von Mises metal plasticity model are examined for the accuracy of deviatoric stress integration of the constitutive equation. The accuracy of stress integration using a strain rate vector for arbitrary direction is presented in terms of an iso-error map for comparison with the exact solution. Accuracy and stability issues of the quadratic integration method are discussed using a two-dimensional metal panel problem with a single slit-like defect in the center. The scale factor and shape factor were introduced to a quadratic integration rule for assuming a returning directional tensor from a trial stress onto the final yield surface. Luckily enough, the perfectly plastic model is the only case where the analytical solution is possible. Thus, solution accuracies were compared with those of the exact solutions. Since the standard scale factor ranges from 0 to 1, which is similar to the linear α -method, the penalty scale factors that are greater than 1 were mainly explored to examine the solution accuracies and computational efficiency. A higher value of scale factor above five shows a better computational efficiency but a decreased solution accuracy, especially in the higher plastification zone. A well-balanced scale factor for both computational efficiency and solution accuracy was found to be between one and five. The trade-off scale factor was proposed to be five. The proper shape factor was also proposed to be {1,1,4}/6 among the different combinations of weight distribution over a time interval. This proposed scale factor and shape factor is also valid for relatively long time periods. Full article
(This article belongs to the Special Issue Constitutive Modelling for Metals)

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