Stress-Strain State of the Composite Based on Spirally Reinforced Filler Under Loading in the Direction of Reinforcement

Abstract

The material under study is based on spirally reinforced filler whose cross-section presents a system of double-periodic elements. Let us isolate a representative element of the material S that consists of a matrix, core and an intermediate layer (Fig. 4.1). Zone S is arranged so that the material cross-section is superimposed by a double-periodic system of the zones coinciding at the overlap with S. In the case of hexagonal packing, the area of zone S for any kind of the element cross-section is $\Omega = 2\sqrt 3$, i.e. it is the area of a rhombus with its vertices in the centers of the four neighboring elements. Areas of the core, matrix and the layer found within S zone are then, correspondingly Ω₁, Ω₃, Ω₂. Let the medium strain in the axis z-direction be 〈ε _z 〉, then [233].