Models of fractional viscous stresses for incompressible materials
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909135202680832 |
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| author | Berjamin, Harold Destrade, Michel |
| author_facet | Berjamin, Harold Destrade, Michel |
| contents | We present and review several models of fractional viscous stresses from the literature, which generalise classical viscosity theories to fractional orders by replacing total strain derivatives in time with fractional time derivatives. We also briefly introduce Prony-type approximations of these theories. Here we investigate the issues of material frame-indifference and thermodynamic consistency for these models and find that on these bases, some are physically unacceptable. Next we study elementary shearing and tensile motions, observing that some models are more convenient to use than others for the analysis of creep and relaxation. Finally, we compute the incremental stresses due to small-amplitude wave propagation in a deformed material, with a view to establish acousto-elastic formulas for prospective experimental calibrations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_01934 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Models of fractional viscous stresses for incompressible materials Berjamin, Harold Destrade, Michel Soft Condensed Matter Mathematical Physics 74S40 (Primary) 74D10, 76A05 (Secondary) We present and review several models of fractional viscous stresses from the literature, which generalise classical viscosity theories to fractional orders by replacing total strain derivatives in time with fractional time derivatives. We also briefly introduce Prony-type approximations of these theories. Here we investigate the issues of material frame-indifference and thermodynamic consistency for these models and find that on these bases, some are physically unacceptable. Next we study elementary shearing and tensile motions, observing that some models are more convenient to use than others for the analysis of creep and relaxation. Finally, we compute the incremental stresses due to small-amplitude wave propagation in a deformed material, with a view to establish acousto-elastic formulas for prospective experimental calibrations. |
| title | Models of fractional viscous stresses for incompressible materials |
| topic | Soft Condensed Matter Mathematical Physics 74S40 (Primary) 74D10, 76A05 (Secondary) |
| url | https://arxiv.org/abs/2305.01934 |