Nonlinear relations of viscous stress and strain rate in nonlinear Viscoelasticity
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910812944203776 |
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| author | Machill, Lennart |
| author_facet | Machill, Lennart |
| contents | We consider a Kelvin-Voigt model for viscoelastic second-grade materials, where the elastic and the viscous stress tensor both satisfy frame indifference. Using a rigidity estimate by [Ciarlet-Mardare '15], existence of weak solutions is shown by means of a frame-indifferent time-discretization scheme. Further, the result includes viscous stress tensors which can be calculated by nonquadratic polynomial densities. Afterwards, we investigate the long-time behavior of solutions in the case of small external loading and initial data. Our main tool is the abstract theory of metric gradient flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11882 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear relations of viscous stress and strain rate in nonlinear Viscoelasticity Machill, Lennart Analysis of PDEs 74A30, 74D10, 35A15, 35Q74, 74G22 We consider a Kelvin-Voigt model for viscoelastic second-grade materials, where the elastic and the viscous stress tensor both satisfy frame indifference. Using a rigidity estimate by [Ciarlet-Mardare '15], existence of weak solutions is shown by means of a frame-indifferent time-discretization scheme. Further, the result includes viscous stress tensors which can be calculated by nonquadratic polynomial densities. Afterwards, we investigate the long-time behavior of solutions in the case of small external loading and initial data. Our main tool is the abstract theory of metric gradient flows. |
| title | Nonlinear relations of viscous stress and strain rate in nonlinear Viscoelasticity |
| topic | Analysis of PDEs 74A30, 74D10, 35A15, 35Q74, 74G22 |
| url | https://arxiv.org/abs/2409.11882 |