# CEE Seminar: Design of New Materials and Structures to Maximize Strength at Probability Tail: A Neglected Challenge for Quasibrittle and Biomimetic Materials

In developing new materials, the research objective has been to maximize the mean strength (or fracture energy) of material or structure and minimize the coefficient of variation. However, for engineering structures such as airframes, bridges of microelectronic devices, the objective should be to maximize the tail probability strength, which is defined as the strength corresponding to failure probability 10-6 per lifetime. Optimizing the strength and coefficient of variation does not guarantee it. The ratio of the distance of the tail point from the mean strength to the standard deviation depends on the architecture and microstructure of the material (governing the safety factor) is what should also be minimized. For the Gaussian and Weibull distributions of strength, the only ones known up to the 1980s, this ratio differs by almost 2:1. For the strength distributions of quasibrittle materials, it can be anywhere in between, depending on material architecture and structure size....