Design of a bio-inspired composite using probabilistic fracture mechanics

Artificial composites inspired from biological materials such as nacre and bone has a staggered structure of hard inclusions surrounded by a soft interface. These composites possess an excellent combination of strength, toughness and stiffness. These properties depends on a critical value of overlap ratio of inclusions, and hence is one of major parameters in the design of bio-inspired composites. Randomness in material and geometrical parameters could exist in such composites. In this work, the randomness in various parameters are considered, and using probabilistic methods, the critical overlap ratio is found out. This is done for two dimensional, and three dimensional inclusions. For the three dimensional case, due to unavailability of the analytical solution, high dimensional model representation technique in conjunction with finite element analysis is done to find out the critical overlap ratio. To determine the probability of failure for two dimensional as well as three dimensional cases, Monte Carlo Simulation is used. Finally, based on the study a factor of safety is proposed for the critical stress intensity factor which could be used in design to account for uncertainties in the various parameters.