‘Explicit’ and ‘implicit’ non-local continuous descriptions for a plate with circular inclusion in tension

Meral Tuna*, Lorenzo Leonetti, Patrizia Trovalusci, Mesut Kirca

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


Increasing application of composite structures in engineering field inherently speed up the studies focusing on the investigation of non-homogeneous bodies. Due to their capability on capturing the size effects, and offering solutions independent of spatial discretization, enriched non-classical continuum theories are often more preferable with respect to the classical ones. In the present study, the sample problem of a plate with a circular inclusion subjected to a uniform tensile stress is investigated in terms of both ‘implicit’/‘weak’ and ‘explicit’/‘strong’ non-local descriptions: Cosserat (micropolar) and Eringen theories, by employing the finite element method. The material parameters of ‘implicit’ model is assumed to be known, while the nonlocality of ‘explicit’ model is optimized according to stress concentration factors reported for infinite Cosserat plates. The advantages/disadvantages, and correspondence/non-correspondence between both non-local models are highlighted and discussed apparently for the first time, by comparing the stress field provided for reference benchmark problem under various scale ratios, and material parameter combinations for matrix-inclusion pair. The results reveal the analogous character of both non-local models in case of geometric singularities, which may pave the way for further studies considering problems with noticeable scale effects and load singularities.

Original languageEnglish
Pages (from-to)927-944
Number of pages18
Issue number4
Publication statusPublished - 1 Apr 2020

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature B.V.


This work was done when Meral Tuna was a Visiting Researcher at DISG, Sapienza University of Rome, with financial support of Italian Ministry of University and Research PRIN 2015, Project 2015JW9NJT (Grant No. B86J16002300001, ID: 10.13039/501100003407) and PRIN 2017 (Grant No. B86J16002300001) “Materials with microstructure: multiscale models for the derivation non-local continua of ‘implicit/weak’ and explicit/strong’” which is gratefully acknowledged.

FundersFunder number
Ministero dell’Istruzione, dell’Università e della Ricerca2015JW9NJT, B86J16002300001
Sapienza Università di Roma


    • Cosserat
    • Eringen
    • Finite elements
    • Non-local models
    • Nonhomogeneous solids
    • Scale effects


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