Modeling of an elastic matrix reinforced with two families of fibers under simple shear: a mimic of annulus fibrosus

A simple model for describing the mechanical behavior of a soft bidirectional-fiber-reinforced composite under simple shear deformation is proposed. Four parameters, including material properties and initial angle of fibers, are required in this model to predict the nonlinear material response. A soft material that was made of silicone rubber and two families of continuous fibers of polypropylene were tested in order to validate the proposed model. Experiments were performed on composite specimens with two distinct fiber orientations. The values of shear strain were evaluated from full-field displacements extracted by the digital image correlation method. The properties of the fibers and the neat matrix were obtained from uniaxial tensile and simple shear tests, respectively. These data were used as input data. The model predictions are in excellent agreement with the experimental data of the elastomeric composite. After validation, the proposed model was used to characterize the shear response of an annulus fibrosus of ovine intervertebral disk, using experimental data from literature. The results indicate that the proposed model is capable of describing the nonlinear response of the annulus fibrosus under simple shear. Moreover, it may be suitable for estimating important mechanical parameters of fibrous soft tissues.