A constitutive model for fibre-matrix interaction in fibre-reinforced hyperelastic materials
The strain energy for incompressible transversely isotropic nonlinearly elastic materials reinforced by a single family of fibres is decomposed into an isotropic part representing the mechanical response of the isotropic matrix and an anisotropic part representing the contribution to the mechanical...
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| Format: | Article |
| Language: | English |
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Elsevier
2020-06-01
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| Series: | Applications in Engineering Science |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S266649682030008X |
| _version_ | 1818461007893233664 |
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| author | C.O. Horgan J.G. Murphy |
| author_facet | C.O. Horgan J.G. Murphy |
| author_sort | C.O. Horgan |
| collection | DOAJ |
| description | The strain energy for incompressible transversely isotropic nonlinearly elastic materials reinforced by a single family of fibres is decomposed into an isotropic part representing the mechanical response of the isotropic matrix and an anisotropic part representing the contribution to the mechanical response from the fibres. It is the form of the anisotropic component that is of interest here. We note that the classical deformation invariants can be divided into two classes: the invariants that are of degree two and those of degree four in the principal stretches. The approach adopted here is straightforward: assume that there is a proportional relationship linking derivatives of the strain energy with respect to invariants of the same degree in the principal stretches in the general stress-strain law. The proportionality constants are interpreted as being measures of the fibre-matrix interaction in transversely isotropic non-linear elasticity. Setting these constants identically zero recovers many of the simplified strain energies commonly found in the literature. It is shown that inclusion of a matrix-fibre interaction can have a significant effect on the mechanical response. An influential method of incorporating fibre dispersion into the modelling procedure is shown to be a special case of the approach introduced here. |
| first_indexed | 2024-12-14T23:39:18Z |
| format | Article |
| id | doaj.art-c4a35dfe84db40f69173661ca3453065 |
| institution | Directory Open Access Journal |
| issn | 2666-4968 |
| language | English |
| last_indexed | 2024-12-14T23:39:18Z |
| publishDate | 2020-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Applications in Engineering Science |
| spelling | doaj.art-c4a35dfe84db40f69173661ca34530652022-12-21T22:43:33ZengElsevierApplications in Engineering Science2666-49682020-06-012100008A constitutive model for fibre-matrix interaction in fibre-reinforced hyperelastic materialsC.O. Horgan0J.G. Murphy1School of Engineering and Applied Science, University of Virginia, Charlottesville, VA 22904, USACorresponding author at: Department of Mechanical Engineering, Dublin City University, Glasnevin, Dublin D09 W6Y4, Ireland.; Department of Mechanical Engineering, Dublin City University, Glasnevin, Dublin D09 W6Y4, Ireland; School of Mathematics, Statistics and Applied Mathematics, National University of Ireland Galway, University Road, Galway, IrelandThe strain energy for incompressible transversely isotropic nonlinearly elastic materials reinforced by a single family of fibres is decomposed into an isotropic part representing the mechanical response of the isotropic matrix and an anisotropic part representing the contribution to the mechanical response from the fibres. It is the form of the anisotropic component that is of interest here. We note that the classical deformation invariants can be divided into two classes: the invariants that are of degree two and those of degree four in the principal stretches. The approach adopted here is straightforward: assume that there is a proportional relationship linking derivatives of the strain energy with respect to invariants of the same degree in the principal stretches in the general stress-strain law. The proportionality constants are interpreted as being measures of the fibre-matrix interaction in transversely isotropic non-linear elasticity. Setting these constants identically zero recovers many of the simplified strain energies commonly found in the literature. It is shown that inclusion of a matrix-fibre interaction can have a significant effect on the mechanical response. An influential method of incorporating fibre dispersion into the modelling procedure is shown to be a special case of the approach introduced here.http://www.sciencedirect.com/science/article/pii/S266649682030008XIncompressibilityNonlinearly elasticTransversely isotropicMatrix-fibre interactionSimple shearPoynting effect |
| spellingShingle | C.O. Horgan J.G. Murphy A constitutive model for fibre-matrix interaction in fibre-reinforced hyperelastic materials Applications in Engineering Science Incompressibility Nonlinearly elastic Transversely isotropic Matrix-fibre interaction Simple shear Poynting effect |
| title | A constitutive model for fibre-matrix interaction in fibre-reinforced hyperelastic materials |
| title_full | A constitutive model for fibre-matrix interaction in fibre-reinforced hyperelastic materials |
| title_fullStr | A constitutive model for fibre-matrix interaction in fibre-reinforced hyperelastic materials |
| title_full_unstemmed | A constitutive model for fibre-matrix interaction in fibre-reinforced hyperelastic materials |
| title_short | A constitutive model for fibre-matrix interaction in fibre-reinforced hyperelastic materials |
| title_sort | constitutive model for fibre matrix interaction in fibre reinforced hyperelastic materials |
| topic | Incompressibility Nonlinearly elastic Transversely isotropic Matrix-fibre interaction Simple shear Poynting effect |
| url | http://www.sciencedirect.com/science/article/pii/S266649682030008X |
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