On the second gradient nonlinear spectral constitutive modelling of viscoelastic composites reinforced with stiff fibers
Abstract General novel nonlinear second-gradient spectral constitutive models for rate dependent fiber-reinforced viscoelastic solids that consider bending stiffness are developed. The constitutive models are characterized by spectral invariants, each with a clearer physical meaning compared to the...
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Nature Portfolio
2025-07-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-025-05230-7 |
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| author | M. H. B. M. Shariff |
| author_facet | M. H. B. M. Shariff |
| author_sort | M. H. B. M. Shariff |
| collection | DOAJ |
| description | Abstract General novel nonlinear second-gradient spectral constitutive models for rate dependent fiber-reinforced viscoelastic solids that consider bending stiffness are developed. The constitutive models are characterized by spectral invariants, each with a clearer physical meaning compared to the classical invariants. Hence, they are experimentally useful if a rigorous experimental curve fitting exercise is used to obtain a specific form of free energy function. The number of complete-irreducible-minimal spectral invariants is significantly less than the number of ‘classical’ complete-irreducible invariants given in the literature, and hence modelling complexity is drastically reduced when a spectral technique is used. Our spectral approach in this paper is different from the classical invariant approach that have been done in the last decades regarding nonlinear solid mechanics. A detailed proof to show that the spherical part of the couple stress is just a Lagrange multiplier, is given. Results for pure bending and, the extension and inflation of a solid cylinder, that could be useful for experiments and numerical validations, are given. |
| format | Article |
| id | doaj-art-c333123c0dac43cd8bfcbf8f1ce0cdeb |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-c333123c0dac43cd8bfcbf8f1ce0cdeb2025-08-20T04:01:34ZengNature PortfolioScientific Reports2045-23222025-07-0115111810.1038/s41598-025-05230-7On the second gradient nonlinear spectral constitutive modelling of viscoelastic composites reinforced with stiff fibersM. H. B. M. Shariff0Department of Applied Mathematics, Khalifa University of Science and TechnologyAbstract General novel nonlinear second-gradient spectral constitutive models for rate dependent fiber-reinforced viscoelastic solids that consider bending stiffness are developed. The constitutive models are characterized by spectral invariants, each with a clearer physical meaning compared to the classical invariants. Hence, they are experimentally useful if a rigorous experimental curve fitting exercise is used to obtain a specific form of free energy function. The number of complete-irreducible-minimal spectral invariants is significantly less than the number of ‘classical’ complete-irreducible invariants given in the literature, and hence modelling complexity is drastically reduced when a spectral technique is used. Our spectral approach in this paper is different from the classical invariant approach that have been done in the last decades regarding nonlinear solid mechanics. A detailed proof to show that the spherical part of the couple stress is just a Lagrange multiplier, is given. Results for pure bending and, the extension and inflation of a solid cylinder, that could be useful for experiments and numerical validations, are given.https://doi.org/10.1038/s41598-025-05230-7Fibre-reinforced solidsNon-linear viscoelasticBending stiffnessSpectral invariants and formulationCouple stress |
| spellingShingle | M. H. B. M. Shariff On the second gradient nonlinear spectral constitutive modelling of viscoelastic composites reinforced with stiff fibers Scientific Reports Fibre-reinforced solids Non-linear viscoelastic Bending stiffness Spectral invariants and formulation Couple stress |
| title | On the second gradient nonlinear spectral constitutive modelling of viscoelastic composites reinforced with stiff fibers |
| title_full | On the second gradient nonlinear spectral constitutive modelling of viscoelastic composites reinforced with stiff fibers |
| title_fullStr | On the second gradient nonlinear spectral constitutive modelling of viscoelastic composites reinforced with stiff fibers |
| title_full_unstemmed | On the second gradient nonlinear spectral constitutive modelling of viscoelastic composites reinforced with stiff fibers |
| title_short | On the second gradient nonlinear spectral constitutive modelling of viscoelastic composites reinforced with stiff fibers |
| title_sort | on the second gradient nonlinear spectral constitutive modelling of viscoelastic composites reinforced with stiff fibers |
| topic | Fibre-reinforced solids Non-linear viscoelastic Bending stiffness Spectral invariants and formulation Couple stress |
| url | https://doi.org/10.1038/s41598-025-05230-7 |
| work_keys_str_mv | AT mhbmshariff onthesecondgradientnonlinearspectralconstitutivemodellingofviscoelasticcompositesreinforcedwithstifffibers |