Isogeometric homogenization analysis of dry woven fabrics involving micro-scale frictional contact

Abstract

With a view to application to micro-macro decoupled multiscale simulations, a method of isogeometric homogenization analysis (IGHA) is proposed to characterize the in-plane macroscopic material behavior of dry woven fabrics in consideration of microscopic frictional-contact between fiber bundles. The microstructure of dry woven fabrics having periodicity only in in-plane directions, which is identified with the representative volume element to realize in-plane macroscopic deformations, is referred to as an in-plane unit cell in this study and is regarded as a virtual specimen in numerical plate testing (NPT). NURBS basis functions are utilized for discretization to accurately solve micro-scale frictional contact problems of fiber bundles and the knot-to-surface (KTS) and mortar-based KTS algorithms are employed to evaluate the contact- and friction-related variables. The initial state of an in-plane unit cells, which is supposed to be obtained by a weaving process, is determined as a solution of the bending problem of two fiber bundles contacting with each other and is in reality subjected to in-plane tension. Several numerical examples are presented to demonstrate the performance and capability of the proposed IGHA for conducting NPT of dry woven fabrics involving with microscale frictional-contact to characterize the geometrical-nonlinearity-induced material nonlinearity especially in response to macroscopic shear deformations.

Keywords

• isogeometric analysis
• frictional-contact
• homogenization
• dry woven fabric
• composite material