Micromechanical modeling of woven and textile composites

Analyses of undulated unidirectional and woven fibrous composites are performed. These analyses are based on a micromechanical approach that takes into account the shapes of the fiber undulation and cross-section in the representative unit cell. The proposed methods are able to predict the generalized elastic properties of the composite (the three dimensional constitutive relations).; The general approach is first established by deriving the layered model and the fibrous model. The layered model is derived for the straight fiber case using a strain energy approach. This model constitutes the first step in the derivation of the fibrous model and the analysis of fiber undulation.; Analysis of each representative unit cell (straight, undulated, unidirectional, and woven) is performed using two different methods. The first method is a direct application of the fibrous model for the straight fiber case. Analysis of the undulation using this method consists of dividing the representative unit cell into infinitesimal sections. Each section is modeled as a fibrous composite having its own properties. This results from transforming the local properties into the global ones using the local angle between the fiber and the global coordinate system. The final properties of the whole unit cell are computed by assembling these sections with an iso-stress condition.; The second method is based on the layered model. In this method, the representative unit cell is divided into sections similar to those of the first method. These sections are further subdivided into infinitesimal pieces where the layered model is applied to each piece individually. For cases with fiber undulation, the fiber properties of each infinitesimal piece are first transformed using the local angle, then the effective properties are computed using the layered model equations. Assembling in this case is carried on with iso-stress and iso-strain conditions to compute the final properties.; The analytical methods derived for all cases are accompanied by finite element modeling and solution. The finite element approach represents, in the absence of experimental techniques, a way of comparing results. In this approach, some of the assumptions used in the derivation of the analytical models are not needed. In order to handle the number of different cases to be analyzed, an automated procedure to build and solve the finite element models is developed. Properties predicted by the different models (analytical and finite element) are found to be in good agreement.; As an application, the free vibration characteristics of thick woven composite plates are studied. Two cases are considered, a plate strip and a rectangular plate. Results of thick plate solution and classical thin plate solution compare well in the low frequency range and small thickness-to-length ratios.