Model prediction of unidirectional fiber-reinforced composites under finite deformation

The intuitive knowledge is that the mechanical modulus of unidirectional fiber-reinforced composites (UD-FRPs) decreases with higher fiber orientation angles. However, numerical results in this work and experimental results in previous literature indicate that the mechanical response of UD-FRPs has a U-shaped dependence on fiber orientation angle. To explain this phenomenon, we develop an anisotropic model to capture the mechanical behavior of UD-FRPs. The strain energy is decomposed into four components: matrix, fiber, fiber-matrix normal, and shear interactions. Each component can be determined by matching the mechanical responses of unit cells with 0°, 45°, and 90° off-axis. The results obtained from the presented model match well with the numerical response of unit cells with 15°, 30°, 60°, and 75° off-axis. With an increasing fiber orientation angle, the matrix part remains unchanged, the fiber component decreases, but the fiber-matrix normal component increases, and the fiber-matrix shear component increases and then decreases. The change in strain energy contributions explains the mechanism of the U-shaped dependence of the mechanical response on fiber orientation angle.