Investigation of buckling modes of sandwich specimens with facing layers from $[0^\circ]_{s}$ fiber-reinforced plastic under axial compression

Analytical solutions to the linearized problems on possible macroscale buckling modes of sandwich specimens made from fiber-reinforced plastics with lay-up sequence $[0^\circ]_{s}$ ($s$ is the number of laminas) under axial compression were analyzed. Materials characterized by a physically nonlinear dependence only between the transverse shear stresses and the corresponding shear strains were considered. Linearized equations of equilibrium in a perturbed state obtained on the basis of the previously constructed geometrically nonlinear equations of the theory of sandwich shells with a transversely flexible core were used. The linearized equations are based on the use of S.P. Timoshenko's refined model for the facing layers, which takes into account the transverse compression, as well as on the use of three-dimensional equations of the theory of elasticity, which are simplified by the model of the transversely flexible layer, for the core. The latter allow integration over the thickness with the introduction of two unknown functions (transverse tangential stresses). In the linearized equations used, the physical nonlinearity of the material of the facing layers was taken into account in accordance with the Shanley concept based on the introduction of the tangential transverse shear modulus. In the equations used, there are degenerate terms that correspond to the implementation of purely transverse-shear buckling modes during compression of the specimen in the axial direction (along the fibers). The implementation of these buckling modes is possible for specimens with a considerable relative thickness of the layers package. Based on the analysis of the results obtained, it was shown that failure for these specimens is most likely due to the buckling in such a macroscale flexural-shear mode, which is predominantly transverse-shear and is realized when the compressive stress averaged over the thickness of the facing layers is equal to the shear modulus of the transverse shear of the composite in the vicinity of the end section of the working length of the specimen in its unperturbed state.