In this paper, a computationally efficient semi-analytical method is developed for the calculation of the elastic micro-fields dominating plain weave composites under remote in-plane loading. The framework needed to obtain analytical displacement estimates is derived using the Rayleigh-Ritz method for a composite plate with spatially varying laminate stiffnesses. The method is developed with the aid of a symmetric woven unit-cell geometry. Three separate boundary value problems, corresponding to remotely applied biaxial and uniaxial displacement, and simple shear boundary conditions are formulated. Unit-cell geometry and material characteristics for both polymer and ceramic matrix composites are incorporated in the formulation of the above boundary value problems.
Extensive solution convergence studies are presented. As expected, convergence is shown to depend on the number of terms used in the Ritz series solution and the number of integration stations used to integrate the spatially laminate stiffnesses within the woven unit-cell geometry. Convergence results for the optimal selection of both of the above parameters are presented. The implications of the method's potential to yield accurate elastic microfields on the evolution of stress induced microdamage in woven systems is discussed.
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