Natural fibres, including flax, hemp, and wood fibres, are employed in various applications like paper, nonwovens, fibre composites, and other biobased materials. Mechanically, a natural fibre can be seen as a complex compound bar with transverse isotropy due to its intricate microstructure. Industrial processing, encompassing both mechanical and chemical steps, causes considerable damage to the fibres, introducing defects like dislocations and microcompressions that significantly influence fibre behaviour. Dumbleton (Tappi 55, 1972) conducted noteworthy cyclic tensile tests on holocellulose summerwood fibres, specifically focusing on fibres with various defect states. %% In these tests, a fibre was positioned between two pre-elongated rubber blankets and then relaxed, inducing longitudinal compression in the fibre. Stress-strain curves were obtained for both nearly defect-free fibres and longitudinally compressed fibres. The nearly defect-free fibre displayed a stiff, almost linear curve, whereas the defective fibre exhibited an S-like stress-strain curve, rupturing at a higher strain but lower stress. The latter also demonstrated an increase in stiffness with each load cycle. Our goal is to develop a model that reproduces the key aspects of Dumbleton's experiment, encompassing both material and structural behaviour. Firstly, we developed a rate-independent material model for orthotropic elasticity and orthotropic plasticity within a hyper-elasto-plastic framework at finite strains. This model is rooted in a covariant formulation featuring plastic-deformation-induced orthotropic evolution. This resulted in constitutive equations capturing evolving orthotropies, akin to the concept of plastic spin, to model the stiffness increase. Secondly, we introduced defect zones into the fibre model through structural modifications, incorporating inclined segments with adjusted hardening in the plastic algorithm. Our numerical results closely match Dumbleton's stress-strain curve data.