IGFEM-based shape sensitivity analysis of the transverse failure of a composite laminate

This manuscript presents a shape sensitivity analysis method based on an Interface-enriched Generalized Finite Element Method (IGFEM) formulation and its application to the sensitivity of the transverse failure of a fiber-reinforced composite laminate with respect to the geometrical parameters that define its microstructure. The analytical sensitivities with respect to individual fiber radius and placement are first derived within the context of a cohesive IGFEM solver specially developed to simulate the fiber/matrix debonding observed in the transverse failure of composite laminates with high fiber volume fraction. The IGFEM solver utilizes \(C^{-1}\) continuous enrichment functions and a cohesive failure model to capture the transverse cracking associated primarily with fiber/matrix interface debonding. In addition to the sensitivities with respect to individual geometrical parameters such as the radius of individual fibers, the sensitivities of the transverse stress–strain response with respect to the parameters that define the distributions of the geometrical parameters such as the mean and standard deviation of the fiber radius and nearest-neighbor distance distributions are also derived. The sensitivity analysis is performed on realistic microstructures composed of hundreds of fibers to characterize the influence of the geometrical parameters and their distributions on the transverse failure response of the composite laminate.