Influence of internal stresses on stability of multilayer micropolar tubes

Within the nonlinear Cosserat continuum, the stability of a compressed multilayer tube under internal and external hydrostatic pressures is studied. The tube is formed by attaching to each other N hollow cylinders that have been subjected to preliminary deformations of axial extension-compression and contains internal stresses. For the model of a physically linear micropolar material, the system of linearized equilibrium equations is derived, which describes the behavior of a multilayer cylindrical tube in a perturbed state. Using a special substitution, the stability analysis is reduced to solving a linear homogeneous boundary-value problem for a system of 6 N ordinary differential equations. In the case of a three-layer tube made of dense polyurethane foam, the stability regions were constructed in the planes of loading parameters (the relative axial compression and the relative external or internal pressure) for different preliminary deformations of inner and outer layers (coatings). According to the results obtained, the preliminary extension of both the outer and inner coatings generally stabilizes the considered deformations of the three-layer tube, while the effect of their preliminary compression is negative. It should be noted here that the pre-stressed outer coating has a more significant influence on the tube stability than the pre-stressed inner coating. In addition, the described effects of preliminary deformations are more pronounced for tubes with thicker coatings.