Explicit expressions for the free-energy and dissipation densities of viscoelastic composites at fixed temperature are proposed. The composites are comprised of an arbitrary number of distinct constituents exhibiting linear Maxwellian rheologies and distributed randomly at a length scale that is much smaller than that over which applied loads vary significantly. Central to their derivation is the recognition that any viscous deformation field can be additively decomposed into an irrotational field and a solenoidal field in such a way that variational approximations available for elastic potentials become applicative to viscoelastic potentials. The thermodynamic potentials conform to a generalized standard model with a finite number of effective internal variables with explicit physical meaning. Specific approximations of the Hashin–Shtrikman and the Self-Consistent types are worked out in detail. Under particular circumstances, these approximations may turn out exact. Macroscopic stress–strain relations and intraphase statistics of the stress field up to second order are also provided.

中文翻译：

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粘弹性复合材料的热力学电位


提出了固定温度下粘弹性复合材料的自由能和耗散密度的显式表达式。复合材料由任意数量的不同成分组成，表现出线性麦克斯韦流变学，并以远小于施加载荷显着变化的长度尺度的长度尺度随机分布。它们推导的核心是认识到任何粘性变形场都可以加法分解为无旋场和螺线管场，这样可用于弹性势的变分近似就可以适用于粘弹性势。热力学势符合广义标准模型，该模型具有有限数量的具有明确物理意义的有效内部变量。详细阐述了 Hashin-Shtrikman 和 Self-Consistent 类型的具体近似值。在特定情况下，这些近似值可能会很精确。还提供了宏观应力-应变关系和应力场的二阶期内统计。