The problem addressed in this study is the full coupling between three different contributions to the strain in thermoviscoelastic composites, elasticity, viscosity and temperature changes. It shows that even in simple situations, the coupling with temperature may lead to counter-intuitive effects which are not accounted for through the sole overall stress–strain relations. The correspondence principle permits to express the macroscopic strain–stress relation and the macroscopic entropy as a set of ordinary differential equations for two types of effective internal variables, mechanical variables on the one hand and thermal variables on the other hand. Interpreting the macroscopic response as a rheological generalized Maxwell model allows us to compute the macroscopic free energy and the dissipated energy of the composite in terms of these internal variables. Coupled with Hashin–Shtrikman estimates, these thermodynamic functions provide additional information on the statistics of the stress field when the composite is subjected to a mixed loading combining mechanical and thermal effects.

中文翻译：

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有效热力学电位和内部变量：颗粒热粘弹性复合材料


本研究解决的问题是热粘弹性复合材料中对应变的三种不同贡献之间的完全耦合，即弹性、粘度和温度变化。它表明，即使在简单的情况下，与温度的耦合也可能导致违反直觉的效果，而这些效果无法通过单独的整体应力-应变关系来解释。对应原理允许将宏观应变-应力关系和宏观熵表示为两种类型的有效内部变量（机械变量和热变量）的一组常微分方程。将宏观响应解释为流变学广义麦克斯韦模型，使我们能够根据这些内部变量计算复合材料的宏观自由能和耗散能。结合 Hashin-Shtrikman 估计，当复合材料受到机械和热效应相结合的混合载荷时，这些热力学函数提供了有关应力场统计的额外信息。