Stress and deformation analysis of fibrous composite materials by point matching

Abstract

SUMMARYThe point matching numerical method and its generalization, the method of boundary point least squares, have been successfully applied to numerous boundary value and eigenvalue problems. The present paper demonstrates the application of these techniques to problems in the micromechanics of fibrous composite materials, i.e. determination of elastic moduli and stress concentrations for parallelfibre materials which are loaded transversely with respect to the fibres. The solution technique utilizes exact solutions of the governing equations of plane elasticity for each component fibre and its surrounding matrix material in a typical repeating section of the composite material. The continuity conditions for stresses and displacements between fibre and matrix and the repeatability conditions at the boundary of the repeating section are satisfied approximately in a pointwise manner. Some special numerical techniques which were found to be particularly useful in applying the point matching method to these problems are delineated. The method is demonstrated for composite materials having circular, elliptical and square fibres in regular, staggered arrays. Numerical results are given which show the accuracy of the method as well as stress concentration and composite elastic moduli data.

Some exact plane elasticity solutions for nonhomogeneous, orthotropic sheets

“…[4]), for purposes of this work moduli will be based upon the "law of mixtures" commonly used for composites. Thus, for example, for a material stressed in the direction (y) of the fibers (Fig.…”

Stress and deformation analysis of fibrous composite materials by point matching

“…u;= u,, v; = vc (20) as depicted in Figure 2. The independent corner displacements in the symmetric case are related to u1 and uz by means of equations (2),(3, (9),(10) and where the integrations are performed piecewise over the fibre and matrix intervals.In the case of shear loading at infinity we haveu;= uc, v; = v, (22) where uc and vB are not independent of each other, but are related by the equations APPLICATION OF THE POINT MATCHING METHOD The solution functions, equations ( 5 ) and…”