A model for elastic hysteresis of unidirectional fibrous nano composites incorporating stick-slip

In fibrous nano-composites, slip of fillers within the matrix comprises a major mechanism through which energy is dissipated. In the current study, a simplified model for predicting the elastic hysteresis of perfectly aligned unidirectional nano-composites loaded in the direction of the fibers is developed. The model, based on shear lag analysis and derived from basic principles of continuum micromechanics, incorporates a shear stick-slip constitutive law at the matrix-fiber interface. Once calibrated by comparison to cyclic stress-strain curves on nano-composites, the model is used to conduct a set of parametric studies on the influence of various parameters on the energy dissipation. Simulation results reveal that the interfacial shear stick-slip constitutive law, the volume fraction andthe aspect ratio of the fibers, and the fiber-to-matrix stiffness ratio have a direct influence on the hysteresis of nano-composites. Also, it is demonstrated that it is possible to achieve an optimal set of parameters for which energy dissipation due to hysteresis is maximized. The proposed model provides a numerically efficient yet reasonably accurate alternative for use in design and analysis of fibrous composites when compared to existing complex models.