Continuous models for analyzing the mechanical behavior of reinforcements in composites

In this chapter two continuous models based on a geometric transformation approach and an energy approach, respectively, for analyzing mechanical behavior of woven fabric composites are proposed. In the geometric transformation approach, a convected coordinate system is taken to describe contravariant stresses and covariant strains. The transformations between the contravariant/covariant components and Cartesian components of the stress and strain tensors provide an approach for deriving a non-orthogonal constitutive relation. In the energy approach, a simple hyperelastic constitutive model is developed. The strain energy function is decomposed into tensile energy from fiber yarn stretches and shearing energy from yarn angular change.