Micromechanics Model Based On Variational Principles Woven Composites

As a multiphase material, woven fabric composites have a significant structural mechanism. The mechanical behavior and failure mechanism of woven fabric composites depend significantly on its micro-structure and the properties of each constituent. It is a new trend to study the relationship between the macro-mechanical behavior and the properties of the constituents as well as the micro-structural parameters. In this paper, the general rules are illustrated to characterize the micro-structure of woven composites by some design parameters. A geometrical structure model of general woven composites is put forward. Based on the above studies, a simple variational principle and a method of Lagrangian multipliers are introduced for the first time to construct the mesomechanic model. Then a new mesomechanic model is presented to predict the mechanical properties of woven composites. The model accounts for fabric geometry, yarn interactions and yarn crisp. First, by constructing a multi-level decomposition scheme, the composites unit cell is split up into matrix and yarn cells. Then, by a multi-step homogenization procedure, a link is established between the external loading and the internal stresses. The principle idea lies in the interpretation that the "stress concentration factors" can be computed at each step by applying the complementary variational principle. In addition to modeling the stress and strain fields, the compliance matrix is computed in this paper using "stress concentration factors". Samples of woven preform and composites are made in the laboratory. At the end, the theoretical predictions of numerical stiffness are compared with the testing results and a good agreement is reported.