17 - Continuous models for analyzing the mechanical behavior of reinforcements in composites

Abstract

In this chapter two continuous models, which are based on a geometric transformation approach and an energy approach, respectively, for analyzing the mechanical behavior of woven fabric reinforcements in composites are proposed. In the geometric transformation approach, a nonorthogonal constitutive model is developed to characterize the anisotropic material behavior of woven composite fabrics under large deformation. A local convected coordinate system, whose in-plane axes are coincident with the weft-and-warp yarns of woven fabrics, is taken to describe contravariant stress components and covariant strain components in a constitutive relation. The transformations between the contravariant/covariant components and the Cartesian components of the stress and strain tensors provide an approach for deriving the global nonorthogonal constitutive relations for woven composite fabrics. In the energy approach, based on fiber-reinforced continuum mechanics theory, a simple hyperelastic constitutive model is developed to characterize the anisotropic nonlinear material behavior of woven composite fabrics under large deformation. The strain energy function for the anisotropic hyperelastic model is additively decomposed into two parts nominally representing the tensile energy from weft-and-warp yarn fiber stretches and shearing energy from fiber–fiber interaction between weft-and-warp yarns, respectively. The two proposed material characterization approaches are demonstrated on a balanced plain weave composite fabric. The equivalent material properties are obtained by matching experimental data of tensile and shearing tests on the woven composite fabric. The development of these continuous models is critical to the ultimate goal, i.e., using numerical simulations to optimize the forming of woven composite fabric sheets.