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arXiv · 2402.04969

Energy of a non-linear viscoelastic model compatible with fractional relaxation

Andrea Giusti·Andrea Mentrelli·Tommaso Ruggeri
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Abstract

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 $\alpha \in (1/2, 1]$ 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.

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Andrea Giusti, Andrea Mentrelli, Tommaso Ruggeri. 2024-02-07. Energy of a non-linear viscoelastic model compatible with fractional relaxation. https://arxiv.org/abs/2402.04969

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