We develop a linear theory of the Cosserat continuum of a special type. This continuum possesses only rotational degrees of freedom. The constitutive equation for the moment stress tensor is the same as for the elastic continuum. The main feature of our model is that the differential equation relating the wryness tensor to the angular velocity vector contains a source term. Thanks to a special choice of the constitutive equation for the source term, we obtain a model of continuum that has some properties of a viscoelastic continuum. Considering such a continuum, we associate the main variables characterizing its stress–strain state with quantities characterizing electrodynamic and thermodynamic processes. Our new model describes all physical processes that were described by using our previous models, but at the same time, it gives us some important results that cannot be obtained in the framework of our previous models. In contrast to the previous model, which is based on Maxwell’s model of a viscoelastic material, the new model allows us to arrive at Maxwell’s equations for conductors without modifying constitutive equations. In addition, the new model describes the conversion of electrical energy into thermal energy due to Joule heat. Furthermore, the new model allows us to obtain the entropy balance equation.

我们开发了一种特殊类型的 Cosserat 连续体的线性理论。该连续体仅具有旋转自由度。弯矩应力张量的本构方程与弹性连续体的本构方程相同。我们模型的主要特征是，将 wryness 张量与角速度矢量相关的微分方程包含源项。由于源项的本构方程的特殊选择，我们获得了具有粘弹性连续体的某些特性的连续体模型。考虑到这样一个连续体，我们将表征其应力-应变状态的主要变量与表征电动力学和热力学过程的量联系起来。我们的新模型描述了使用我们以前的模型描述的所有物理过程，但同时，它给了我们一些在我们以前的模型框架中无法获得的重要结果。与基于麦克斯韦粘弹性材料模型的先前模型相比，新模型允许我们在不修改本构方程的情况下得出导体麦克斯韦方程。此外，新模型还描述了焦耳热将电能转化为热能的过程。此外，新模型允许我们获得熵平衡方程。新模型描述了焦耳热将电能转化为热能的过程。此外，新模型允许我们获得熵平衡方程。新模型描述了焦耳热将电能转化为热能的过程。此外，新模型允许我们获得熵平衡方程。