Energy of a non-linear viscoelastic model compatible with fractional relaxation
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910321652793344 |
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| author | Giusti, Andrea Mentrelli, Andrea Ruggeri, Tommaso |
| author_facet | Giusti, Andrea Mentrelli, Andrea Ruggeri, Tommaso |
| contents | Recently, a non-linear model of viscoelasticity based on Rational Extended Thermodynamics was proposed in [arXiv:2312.05116]. This theory extends the evolution of the viscous stress beyond the linear framework of the Maxwell model to the non-linear realm, provided that the viscous energy function is given. This work aims at establishing a possible constitutive law for the viscous energy such that the relaxation modulus of the fractional Maxwell model of order $α\in (1/2, 1]$ is contained within the solutions of the (non-linear) relaxation experiment. Necessary and sufficient conditions for the existence of this coincident solution are discussed, together with a numerical evaluation of the viscous energy associated with the non-linear model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04969 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Energy of a non-linear viscoelastic model compatible with fractional relaxation Giusti, Andrea Mentrelli, Andrea Ruggeri, Tommaso Mathematical Physics 35L60, 74A20, 74D10, 33E12 Recently, a non-linear model of viscoelasticity based on Rational Extended Thermodynamics was proposed in [arXiv:2312.05116]. This theory extends the evolution of the viscous stress beyond the linear framework of the Maxwell model to the non-linear realm, provided that the viscous energy function is given. This work aims at establishing a possible constitutive law for the viscous energy such that the relaxation modulus of the fractional Maxwell model of order $α\in (1/2, 1]$ is contained within the solutions of the (non-linear) relaxation experiment. Necessary and sufficient conditions for the existence of this coincident solution are discussed, together with a numerical evaluation of the viscous energy associated with the non-linear model. |
| title | Energy of a non-linear viscoelastic model compatible with fractional relaxation |
| topic | Mathematical Physics 35L60, 74A20, 74D10, 33E12 |
| url | https://arxiv.org/abs/2402.04969 |