A new explicitly solvable model of a unidirectional composite with nonlinear deformable fibers is introduced in this paper. This model generalizes the shear-lag model by including the nonlinear behavior of fibers. The equations of the model allow a Lax representation. This establishes the existence of an infinite number of invariants. The present theory is unique in that the analytical solution of the boundary value problem for simultaneous nonlinear differential equations is reduced to simultaneous nonlinear equations in terms of the boundary values of unknown functions. The two-dimensional multifilament failure problems of unidirectional fiber composites are analyzed. Example numerical solutions that focus specifically on the stress concentration factors of fibers adjacent to the local imperfections and the cracks are discussed.
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