Dynamic shear-lag model for understanding the role of matrix in energy dissipation in fiber-reinforced composites

Lightweight and high impact performance composite design is a big challenge for scientists and engineers. Inspired from well-known biological materials, e.g., the bones, spider silk, and claws of mantis shrimp, artificial composites have been synthesized for engineering applications. Presently, the design of ballistic resistant composites mainly emphasizes the utilization of light and high-strength fibers, whereas the contribution from matrix materials receives less attention. However, recent ballistic experiments on fiber-reinforced composites challenge our common sense. The use of matrix with "low-grade" properties enhances effectively the impact performance. In this study, we establish a dynamic shear-lag model to explore the energy dissipation through viscous matrix materials in fiber-reinforced composites and the associations of energy dissipation characteristics with the properties and geometries of constituents. The model suggests that an enhancement in energy dissipation before the material integrity is lost can be achieved by tuning the shear modulus and viscosity of a matrix. Furthermore, our model implies that an appropriately designed staggered microstructure, adopted by many natural composites, can repeatedly activate the energy dissipation process and thus improve dramatically the impact performance. This model demonstrates the role of matrix in energy dissipation, and stimulates new advanced material design concepts for ballistic applications.Biological composites found in nature often possess exceptional mechanical properties that man-made materials haven't be able to achieve. For example, it is predicted that a pencil thick spider silk thread can stop a flying Boeing airplane. Here, by proposing a dynamic shear-lag model, we investigate the relationships between the impact performance of a composite with the dimensions and properties of its constituents. Our analysis suggests that the impact performance of fiber-reinforced composites could improve surprisingly with "low-grade" matrix materials, and discontinuities (often regarded as "defects") may play an important role in energy dissipation. Counter-intuitive as it may seem, our work helps understanding the secrets of the outstanding dynamic properties of some biological materials, and inspire novel ideas for man-made composites.