Stress distribution in multilayered composite material with curved structures (model of a piecewise homogeneous body)

Abstract

In the case of single-phase (antiphase) curvature in the structure of the composite under consideration, an increase of concentration of the filler entails a decrease (increase) of the values of the self-balanced normal stresses and, conversely, an increase (decrease) of the values of the self-balanced tangential stresses. With η(2) ≤ 0.1 (where η(2) is the concentration of the filler) a decrease of the parameter k=2πH(2)/l (where 2H(2) is the thickness of the layer of filler, l is the wavelength of the forms of curvature) entails a monotonic increase of the self-balanced tangential stress in the case of single-phase curvature. This means that with fixed wavelength of the forms of curvature (with fixed thickness of the layer of filler) a decrease in thickness of the layer of filler (an increase of the wavelength of the forms of curvature) entails a monotonic increase of the tangential stress. The correlation between the self-balanced normal stresses and the parameter k in the case of antiphase curvature with all the considered values (0.02 ≤ η(2) ≤0.5) is nonmonotonic. It follows that with fixed l there exists such a thickness of the layer of filler H(2) at which the self-balanced normal stress σnn has its maximal value. With increasing ratio of the moduli of elasticity of the material of the filler and of the matrix, and also with increasing parameter e=L/l (where L is the length of the sagitta), the values of the self-balanced normal and tangential stresses in both cases under consideration increase. When the curvatures in the structure of the investigated composite materials are very small, the normal stress (in the case of antiphase curvature) and the selfbalanced tangential stress (in the case of single-phase curvature) may be a multiple of the normal stress σ11(1)0 in the matrix which acts in the direction of the Ox1 axis and is balanced by the external forces 〈p〉.