Mathematical modelling and homogenization of thin fiber-reinforced hydrogels
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918316168183808 |
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| author | Chakrabortty, Amartya Dutta, Haradhan Mahato, Hari Shankar |
| author_facet | Chakrabortty, Amartya Dutta, Haradhan Mahato, Hari Shankar |
| contents | This work considers simultaneous homogenization dimension reduction of a poroelastic model for thin fiber-reinforced hydrogels. The analysed medium is defined as a two-component system consisting of a continuous fiber framework with hydrogel inclusions arranged periodically throughout. The fibers are assumed to operate under quasi-stationary linear elasticity, whereas the hydrogel's hydromechanical behavior is represented using Biot's linear poroelasticity model. The asymptotic limit of the coupled system is established when the periodicity and thickness parameters are of the same order and tend to zero simultaneously, utilizing the re-scaling unfolding operator. It is demonstrated that the limit displacement exhibits Kirchhoff-Love-type behavior using the decomposition of plate displacements. Towards the end, a unique solution for the macroscopic problem has been demonstrated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12828 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mathematical modelling and homogenization of thin fiber-reinforced hydrogels Chakrabortty, Amartya Dutta, Haradhan Mahato, Hari Shankar Analysis of PDEs 35B27, 35B40, 35C20, 74Q15, 74S20, 74A15 This work considers simultaneous homogenization dimension reduction of a poroelastic model for thin fiber-reinforced hydrogels. The analysed medium is defined as a two-component system consisting of a continuous fiber framework with hydrogel inclusions arranged periodically throughout. The fibers are assumed to operate under quasi-stationary linear elasticity, whereas the hydrogel's hydromechanical behavior is represented using Biot's linear poroelasticity model. The asymptotic limit of the coupled system is established when the periodicity and thickness parameters are of the same order and tend to zero simultaneously, utilizing the re-scaling unfolding operator. It is demonstrated that the limit displacement exhibits Kirchhoff-Love-type behavior using the decomposition of plate displacements. Towards the end, a unique solution for the macroscopic problem has been demonstrated. |
| title | Mathematical modelling and homogenization of thin fiber-reinforced hydrogels |
| topic | Analysis of PDEs 35B27, 35B40, 35C20, 74Q15, 74S20, 74A15 |
| url | https://arxiv.org/abs/2501.12828 |