A specialized finite element for the study of woven composites

 A specialized finite element is developed for the study of woven composites. The element utilizes an asymptotic displacement expansion comprised of the homogenized displacements and the local micro-displacements associated with the woven unit-cell elasto-statics. Basic trigonometric functions first developed in [1], are employed as solutions to the local woven unit-cell problem under a general state of in-plane loading. The formulation also incorporates robust unit-cell geometry models for both polymer and ceramic matrix woven systems. As a result, the element can be used to predict not only the macroscopic homogeneous elastic response but also the microscopic elastic response of a finite geometry of a woven composite subjected to a general in-plane as well as transverse bending loading. The element performance is demonstrated by solving the finite geometry uni-axial tension problem and via near-tip studies for a crack under mode-I, mode-II, and mixed mode fracture conditions. In each case, the specialized element predictions are compared to known solutions for a corresponding cracked orthotropic material subjected to the same macroscopic loading conditions as well as the approximate solutions obtained using the well established 4-noded isoparametric plane elasticity element.