A non-second-gradient model for nonlinear elastic bodies with fibre stiffness
Abstract In the past, to model fibre stiffness of finite-radius fibres, previous finite-strain (nonlinear) models were mainly based on the theory of non-linear strain-gradient (second-gradient) theory or Kirchhoff rod theory. We note that these models characterize the mechanical behaviour of polar t...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2023-04-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-33670-6 |
| _version_ | 1797841073778720768 |
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| author | M. H. B. M. Shariff J. Merodio R. Bustamante |
| author_facet | M. H. B. M. Shariff J. Merodio R. Bustamante |
| author_sort | M. H. B. M. Shariff |
| collection | DOAJ |
| description | Abstract In the past, to model fibre stiffness of finite-radius fibres, previous finite-strain (nonlinear) models were mainly based on the theory of non-linear strain-gradient (second-gradient) theory or Kirchhoff rod theory. We note that these models characterize the mechanical behaviour of polar transversely isotropic solids with infinitely many purely flexible fibres with zero radius. To introduce the effect of fibre bending stiffness on purely flexible fibres with zero radius, these models assumed the existence of couple stresses (contact torques) and non-symmetric Cauchy stresses. However, these stresses are not present on deformations of actual non-polar elastic solids reinforced by finite-radius fibres. In addition to this, the implementation of boundary conditions for second gradient models is not straightforward and discussion on the effectiveness of strain gradient elasticity models to mechanically describe continuum solids is still ongoing. In this paper, we develop a constitutive equation for a non-linear non-polar elastic solid, reinforced by embedded fibers, in which elastic resistance of the fibers to bending is modelled via the classical branches of continuum mechanics, where the development of the theory of stresses is based on non-polar materials; that is, without using the second gradient theory, which is associated with couple stresses and non-symmetric Cauchy stresses. In view of this, the proposed model is simple and somewhat more realistic compared to previous second gradient models. |
| first_indexed | 2024-04-09T16:25:08Z |
| format | Article |
| id | doaj.art-5bdcf236feeb4b50948715c1f9a4beba |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-04-09T16:25:08Z |
| publishDate | 2023-04-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-5bdcf236feeb4b50948715c1f9a4beba2023-04-23T11:14:52ZengNature PortfolioScientific Reports2045-23222023-04-0113111010.1038/s41598-023-33670-6A non-second-gradient model for nonlinear elastic bodies with fibre stiffnessM. H. B. M. Shariff0J. Merodio1R. Bustamante2Department of Mathematics, Khalifa University of Science and TechnologyDepartamento de Matemática Aplicada a las TIC, ETS de Ingeniería de Sistemas Informáticos, Universidad Politécnica de MadridDepartamento de Ingeniería Mecánica, Universidad de ChileAbstract In the past, to model fibre stiffness of finite-radius fibres, previous finite-strain (nonlinear) models were mainly based on the theory of non-linear strain-gradient (second-gradient) theory or Kirchhoff rod theory. We note that these models characterize the mechanical behaviour of polar transversely isotropic solids with infinitely many purely flexible fibres with zero radius. To introduce the effect of fibre bending stiffness on purely flexible fibres with zero radius, these models assumed the existence of couple stresses (contact torques) and non-symmetric Cauchy stresses. However, these stresses are not present on deformations of actual non-polar elastic solids reinforced by finite-radius fibres. In addition to this, the implementation of boundary conditions for second gradient models is not straightforward and discussion on the effectiveness of strain gradient elasticity models to mechanically describe continuum solids is still ongoing. In this paper, we develop a constitutive equation for a non-linear non-polar elastic solid, reinforced by embedded fibers, in which elastic resistance of the fibers to bending is modelled via the classical branches of continuum mechanics, where the development of the theory of stresses is based on non-polar materials; that is, without using the second gradient theory, which is associated with couple stresses and non-symmetric Cauchy stresses. In view of this, the proposed model is simple and somewhat more realistic compared to previous second gradient models.https://doi.org/10.1038/s41598-023-33670-6 |
| spellingShingle | M. H. B. M. Shariff J. Merodio R. Bustamante A non-second-gradient model for nonlinear elastic bodies with fibre stiffness Scientific Reports |
| title | A non-second-gradient model for nonlinear elastic bodies with fibre stiffness |
| title_full | A non-second-gradient model for nonlinear elastic bodies with fibre stiffness |
| title_fullStr | A non-second-gradient model for nonlinear elastic bodies with fibre stiffness |
| title_full_unstemmed | A non-second-gradient model for nonlinear elastic bodies with fibre stiffness |
| title_short | A non-second-gradient model for nonlinear elastic bodies with fibre stiffness |
| title_sort | non second gradient model for nonlinear elastic bodies with fibre stiffness |
| url | https://doi.org/10.1038/s41598-023-33670-6 |
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