Analytical study on elastic transition in short-fiber composites for plane strain case

An analytical approach for short-fiber-reinforced composites is developed for three-dimensional (3D) elastic stress field distribution subjected to an applied axial load. Two sets of exact displacement solutions for matrix and fiber, which are respectively called far-field and transient solutions, are derived based on the theory of elasticity. The superposition state of these solutions are then used to obtain the analytical expressions for the 3D stress field components over the entire composite system, including the fiber end region, through the adding imaginary fiber technique. The fiber/matrix 3D stress field components fully satisfy the equilibrium and compatibility conditions in the theory of elasticity. The stress field components also satisfy the overall boundary, interface continuity, and axial force equilibrium conditions. The analytical results obtained are then validated by finite element method modeling.