Method of continuous dipoles for modeling of materials reinforced by short micro-fibers

Method of continuous dipoles for modeling of the interaction of composites reinforced with fibers is presented in the paper. The dipoles are distributed along the fiber axis. All three components of dipoles are used to satisfy the boundary conditions along the fiber boundaries. The boundary conditions in strain components instead of displacements are used in the model, which simplifies the numerical solution. In resulting quasi-hyper-singular integral equations the integration is performed analytically. The dipole fields decay in infinity and they accurately simulate the near and far field interaction. The presented models are applicable to solution of problems of composites reinforced by straight fibers with large aspect ratio, which are most significant for practical purposes, as the fibers have large stiffness in tension, but not in bending. The fiber is considered to be rigid in the fiber axis direction.