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...
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
Elsevier
2020
|
| Materias: | |
| Acceso en línea: | https://doaj.org/article/c4a35dfe84db40f69173661ca3453065 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| id |
oai:doaj.org-article:c4a35dfe84db40f69173661ca3453065 |
|---|---|
| record_format |
dspace |
| spelling |
oai:doaj.org-article:c4a35dfe84db40f69173661ca34530652021-12-01T05:05:19ZA constitutive model for fibre-matrix interaction in fibre-reinforced hyperelastic materials2666-496810.1016/j.apples.2020.100008https://doaj.org/article/c4a35dfe84db40f69173661ca34530652020-06-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S266649682030008Xhttps://doaj.org/toc/2666-4968The 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.C.O. HorganJ.G. MurphyElsevierarticleIncompressibilityNonlinearly elasticTransversely isotropicMatrix-fibre interactionSimple shearPoynting effectEngineering (General). Civil engineering (General)TA1-2040ENApplications in Engineering Science, Vol 2, Iss , Pp 100008- (2020) |
| institution |
DOAJ |
| collection |
DOAJ |
| language |
EN |
| topic |
Incompressibility Nonlinearly elastic Transversely isotropic Matrix-fibre interaction Simple shear Poynting effect Engineering (General). Civil engineering (General) TA1-2040 |
| spellingShingle |
Incompressibility Nonlinearly elastic Transversely isotropic Matrix-fibre interaction Simple shear Poynting effect Engineering (General). Civil engineering (General) TA1-2040 C.O. Horgan J.G. Murphy A constitutive model for fibre-matrix interaction in fibre-reinforced hyperelastic materials |
| 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. |
| format |
article |
| author |
C.O. Horgan J.G. Murphy |
| author_facet |
C.O. Horgan J.G. Murphy |
| author_sort |
C.O. Horgan |
| title |
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_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_sort |
constitutive model for fibre-matrix interaction in fibre-reinforced hyperelastic materials |
| publisher |
Elsevier |
| publishDate |
2020 |
| url |
https://doaj.org/article/c4a35dfe84db40f69173661ca3453065 |
| work_keys_str_mv |
AT cohorgan aconstitutivemodelforfibrematrixinteractioninfibrereinforcedhyperelasticmaterials AT jgmurphy aconstitutivemodelforfibrematrixinteractioninfibrereinforcedhyperelasticmaterials AT cohorgan constitutivemodelforfibrematrixinteractioninfibrereinforcedhyperelasticmaterials AT jgmurphy constitutivemodelforfibrematrixinteractioninfibrereinforcedhyperelasticmaterials |
| _version_ |
1718405568573472768 |