Load Diffusion and Absorption Problems From a Finite Fiber to Elastic Infinite Matrix

Abstract

The load transfer behavior of a finite fiber perfectly bonded to an infinite matrix of distinct elastic moduli is investigated in this paper. The fiber is subjected to the uniformly distributed loading applied at infinity or on one cross-section of the fiber. The stress disturbance due to the existing fiber is simulated by the equivalent inclusion method, which formulates the inhomogeneity problem to a system of integral equations. By dividing the fiber into finite numbers of ring elements with uniform distributed eigenstrains, the integral equations can be further reduced to a system of algebraic equations with coefficients expressed in terms of the integrals of Lipschitz-Hankel type. Numerical results are presented for resultant axial force for various fiber length and material properties. The limiting cases of the infinite and semi-infinite fibers are also compared with the exact and approximate solutions.