Crack propagation in a long fiber composite material typically involves the development of a fiber bridging which connects the two crack tips, resulting in an increase of the crack-growth resistance, known as the R-curve effect. The specific contribution of this paper is to account for this effect within the framework of simple one dimensional models and to perform efficient, simple, and complete numerical simulations of crack propagation taking into account creation and transport of the fiber nesting. The composite sample is modelled by an assembly of three beams and a density of damageable springs for the fiber bridging. With this type of modelling, we can separate the global dissipation in the sample into two specific terms: one associated with crack tip propagation and one with degradation of the fiber nesting. We present results for classical Mode I and Mode II tests, using Double Cantilever Beam and End Load Split specimens.