Flat internal buckling modes of fibrous composite elements under tension and compression at the micrometer and millimeter levels

This paper proposes a refined formulation of linearized problems of internal nonuniformly scaled flat buckling modes of a rigid monolayer consisting of fibers and fiber bundles with allowance for their interaction with the surrounding matrix. Fibers are the structural elements of fibrous composites and in a subcritical (unperturbed) state under the action of shear stresses and tensile (compression) stresses in the transverse direction. The problems are formulated using equations constructed by reducing the version of geometrically nonlinear equations of the elasticity theory to one-dimensional equations of the theory of rectilinear rods. These equations are based on the use of the refined Timoshenko shear model with allowance for tension-compression strains in the transverse direction for the rigid monolayer and the transverse-soft layer model with immobile boundary planes in a perturbed state for the epoxy layers. It is shown that loading samples with a structure is accompanied by constant changes in the composite structure due to implementation and alternation of the internal buckling modes with a varying wave formation parameter. This particularly allows explaining the changing of the effective shear modulus of the fibrous composite with increasing shear strains.