A three-constituent multicontinuum theory for woven fabric composite materials

Multicontinuum theory (MCT) refers to the use of phase averaged constituent stress/strain fields for predicting failure in composite structural analysis. Given the composite material mechanical properties as well as those of the constituents, well known closed form algebraic expressions exist to decompose the composite stress/strain fields down to the constituent level. Recent research indicates constituent based failure algorithms show a great deal of promise in predicting material failure when coupled to nonlinear finite element codes. A limitation of MCT is that the traditional constituent decomposition is only valid for materials composed of two constituents. In this paper, the MCT decomposition is generalized to handle composite materials composed of three constituents. The application of interest is a woven fabric composite material. The three constituents consist of the warp bundles, fill bundles, and pure matrix pockets. Numerical results are presented for the proposed three-constituent decomposition and are shown to be in good agreement with phase averaged stresses obtained from direct volume averaging of finite element micromechanics models.