标题： 非线性粘弹性模型的分数松弛兼容能量 显示英文标题

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

摘要： 最近，在[arXiv:2312.05116]中提出了一种基于理性扩展热力学的非线性粘弹性模型。 该理论在给定粘性能量函数的情况下，将粘性应力的演化从麦克斯韦模型的线性框架扩展到非线性领域。 这项工作旨在建立一种可能的粘性能量本构定律，使得分数阶麦克斯韦模型的松弛模量$\alpha \in (1/2, 1]$被包含在（非线性）松弛实验的解中。 讨论了这种重合解存在的必要和充分条件，并对与非线性模型相关的粘性能量进行了数值评估。 显示英文摘要

摘要： 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.