Some gradient theories in linear visco-elastodynamics towards dispersion and attenuation of waves in relation to large-strain models
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910284345507840 |
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| author | Roubíček, Tomáš |
| author_facet | Roubíček, Tomáš |
| contents | Various spatial-gradient extensions of standard viscoelastic rheologies of the Kelvin-Voigt, Maxwell's, and Jeffreys' types are analyzed in linear one-dimensional situations as far as the propagation of waves and their dispersion and attenuation. These gradient extensions are then presented in the large-strain nonlinear variants where they are sometimes used rather for purely analytical reasons either in the Lagrangian or the Eulerian formulations without realizing this wave-propagation context.The interconnection between these two modeling aspects is thus revealed in particular selected cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05089 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Some gradient theories in linear visco-elastodynamics towards dispersion and attenuation of waves in relation to large-strain models Roubíček, Tomáš Fluid Dynamics Analysis of PDEs 35Q74, 74A30, 74B20, 74J05, 76N30 Various spatial-gradient extensions of standard viscoelastic rheologies of the Kelvin-Voigt, Maxwell's, and Jeffreys' types are analyzed in linear one-dimensional situations as far as the propagation of waves and their dispersion and attenuation. These gradient extensions are then presented in the large-strain nonlinear variants where they are sometimes used rather for purely analytical reasons either in the Lagrangian or the Eulerian formulations without realizing this wave-propagation context.The interconnection between these two modeling aspects is thus revealed in particular selected cases. |
| title | Some gradient theories in linear visco-elastodynamics towards dispersion and attenuation of waves in relation to large-strain models |
| topic | Fluid Dynamics Analysis of PDEs 35Q74, 74A30, 74B20, 74J05, 76N30 |
| url | https://arxiv.org/abs/2309.05089 |