Stability of circular micropolar rod with prestressed two-layer coating

Abstract

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.