Within the framework of the Cosserat continuum, the stability of a compressed circular rod with a two-layer coating is studied. It is assumed that the coating layers were fixed to each other and attached to the rod after preliminary deformations of axial extension–compression and contain internal stresses. For the physically linear model of a micropolar material, the linearized equilibrium equations are derived, which describes the behavior of the considered composite structure in a perturbed state. By solving them for the rod and coating made of dense polyurethane foam, the critical axial compression is determined for different initial deformations of the layers. According to the results obtained, the preliminary extension of both the outer and inner coating layers stabilizes the deformation of axial compression of the rod, while the effect of their preliminary compression is generally negative. Moreover, with a sufficiently strong initial compression of one of the layers, the buckling of the rod is possible in the absence of its deformation solely due to internal stresses in the coating. Additionally, it was found that the stability of the considered composite structure increases with a decrease in its overall size (scale). This effect is due to the influence of the material microstructure and is not observed in the classical (non-polar) elasticity.

在Cosserat连续体的框架内，研究了具有两层涂层的压缩圆棒的稳定性。假设涂层在轴向拉伸压缩的初步变形后彼此固定并附着在棒上，并且包含内部应力。对于微极性材料的物理线性模型，导出了线性平衡方程，该方程描述了所考虑的复合结构在扰动状态下的行为。通过求解由致密聚氨酯泡沫制成的杆和涂层，可以确定不同层初始变形的临界轴向压缩力。根据获得的结果，外涂层和内涂层的初步扩展可稳定杆的轴向压缩变形，而其初步压缩的效果通常是负面的。而且，在其中一层的足够强的初始压缩的情况下，杆的屈曲是可能的，而没有杆的变形，这仅仅是由于涂层中的内应力引起的。另外，发现所考虑的复合结构的稳定性随着其整体尺寸（规模）的减小而增加。这种影响是由于材料微观结构的影响，在经典（非极性）弹性中没有观察到。已经发现，所考虑的复合结构的稳定性随着其整体尺寸（尺度）的减小而增加。这种影响是由于材料微观结构的影响，在经典（非极性）弹性中没有观察到。已经发现，所考虑的复合结构的稳定性随着其整体尺寸（尺度）的减小而增加。这种影响是由于材料微观结构的影响，在经典（非极性）弹性中没有观察到。