The decay rate of the edge effect in a material reinforced with fibers of square cross-section and subjected to transverse uniaxial deformation is studied. The case of uniform loading of near-surface fibers is considered. The edge effect is analyzed by numerically solving a boundary-value problem of elasticity for inhomogeneous bodies and applying a quantitative decay criterion for normal stresses Keywords: edge effect, decay rate, fibrous material, piecewise-homogeneous body model, quantitative criterion, base scheme, discrete model
Introduction.A task of current importance in the statics of composites is to gain insight into the edge effects in a composite under various loading conditions, taking into account its microstructure [1-5, 9, 12]. Design models for analysis of the decay of edge effects in layered materials with isotropic components under a surface load applied either along or normally to the layers were discussed in [5]. The former type of loading results in the maximum decay length of the edge effect for a representative element of the material, compared with other types of loading. When the load acts in the reinforcement direction, the decay length of the edge effect may be severalfold greater than the typical length of the load application region. In the latter case of loading, the decay length is comparable with the size of the load application region. In [1][2][3]9], a plane problem was solved to determine the edge effect in a layered material with reinforcement layers subjected to uniaxial longitudinal compression, which is the first type of loading mentioned above. The joint effect of the external load and the structure of the material on the decay of the edge effect was analyzed for different spatial periods of the surface load compared with the total thickness of the reinforcement and matrix layers (structure parameter of the material). It was discovered that when the reinforcement layers are subject to uniform longitudinal compression, the maximum length of the edge effect, determined to within 1%, is on the order of one to two structure parameters.In the present paper, we solve a plane problem to determine the decay parameters of the edge effect in a material reinforced with unidirectional rectilinear fibers of square cross-section and subjected to uniaxial transverse compression. We will examine the case where near-surface fibers are under uniform loading. The loading conditions in this problem are of the second type mentioned above (load is perpendicular to the reinforcement direction). Since the problem to be solved is plane, we will use the term "square inclusion" instead of "fiber of square cross-section."Note that when a layered material deforms longitudinally and the edge effect extends along continuous layers, stresses change monotonically and the stress state in each component of the material becomes homogeneous upon decay of the edge effect. A feature of the problem under consideration is that the stresses vary nonmonotonically as the edge effect decays (this is because of the in...