HYPERELASTIC SHEAR LAG MODEL

Based on the analysis of deformation of a representative volume, a micromechanical model is derived to describe the elastic modulus of a composite reinforced with unidirectional short fibers under tension in the reinforcement direction. The analysis includes an exact solution to the hyperelastic equations for the deformed matrix and an approximate solution to the equations for the fiber material. The solution is provided for a Neo-Hookean material. Formulae are derived to relate the elastic strain energy with the macroscopic longitudinal strain of the composite, as well as to describe the longitudinal and radial deformation of the matrix and fiber material. The main result is a formula that relates the initial tangential elastic modulus of the composite (an analog of Young's modulus in linear elasticity) to the mechanical characteristics of the composite constituents (namely, the ratio of the elastic moduli of the matrix and fiber), as well as to the geometric characteristics (length-to-diameter ratio) and volume fraction of fibers in the composite. The derived results are compared with the findings of other analytical models, as well as with the known results of numerical simulation by the finite element and boundary element methods. The results generalize the well-known shear lag (SL) model to hyperelastic materials and are obtained using a more rigorous analysis than the original model.