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 microdisplacements associated with the woven unit-cell elastostatics. 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 uniaxial 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.