Dr. Zdeněk P. Bažant provided a lecture at RIME Group

Date: on April 25, 2018

Dr. Zdeněk P. Bažant, McCormick Institute Professor and Walter P. Murphy Professor of CEE Engineering, Mechanical Engineering and Material Science Engineering, presented a seminar entitled “Design of New Materials and Structures to Maximize Strength at Probability Tail: A NEGLECTED CHALLENGE FOR QUASIBRITTLE AND BIOMIMETIC MATERIALS” at RIME Group on Wednesday, April 25, 2018 as a part of Rutgers CEE Department Seminar Series.

Below is the Abstract excerpted from his presentation.

Abstract: In developing new materials, the research objective has been to maximize the mean strength (or fracture energy) of material or structure. However, for engineering structures such as airframes or bridges, the objective should be to maximize the tail probability strength, which is defined as the strength corresponding to failure probability 10-6 per lifetime. 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 and is what should be minimized. For the Gaussian and Weibull distributions of strength, the only ones known up to the 1980s, this ratio is almost 2:1. For the strength distributions of quasibrittle materials, it can be anywhere in between, depending on material architecture and structure size. These materials, characterized by a nonnegligible size of the fracture process zone, include concretes, rocks, tough ceramics, fiber composites, stiff soils, sea ice, snow slabs, rigid foams, bone, dental material, many bio-materials, etc. A theory to deduce the strength distribution tail from atomistic crack jumps and Kramer’s rule of transition state theory, and determine the multiscale transition to the representative volume element (RVE) of material, is briefly reviewed. The strength distribution of quasi-brittle particulate or fibrous materials, whose size is proportional to the number of RVEs, is obtained from the weakest-link chain with a finite number of links and is characterized by a Gauss-Weibull grafted distribution. Comparisons with observed strength histograms and size effect curves are demonstrated. Discussion then turns to new results on biomimetic imbricated (or scattered) lamellar systems, exemplified by nacre, whose mean strength exceeds the strength of constituents by an order of magnitude. The nacreous quasi-brittle material is simplified as a fishnet pulled diagonally, which makes possible an analytical solution of the strength probability distribution. The solution is verified by millions of Monte-Carlo simulations of fishnets of various shapes and sizes. After the weakest-link model and the fiber-bundle model, the fishnet is the third strength probability model that is amenable to an analytical solution. It is found that, in addition to the well-known effect on the mean strength, the nacreous micro-structure provides an additional strengthening at the strength probability tail. The most important consequence of the quasi-brittleness, and also the most useful way of calibration, is the size effect on mean structure strength.