Physics and fracture

Abstract

Attempting to understand the relevant material properties that are vital to an object's construction is as old as humankind itself, and today, it justifies the intense research effort that goes under the label of materials science. An important subfield of materials science is the study of how materials react to external forces. Some materials fracture, for instance, whereas others flow: a glass rod will break if bent strongly enough, but a lead rod will simply change its shape internally. The importance of these questions can't be overemphasized - the probability of finding a crack that is at least 5 centimeters long in any randomly chosen commercial aircraft is 50 percent, for example; how can we be sure that this isn't dangerous? How can we trust that a given high-rise building is safe? Such questions touch our lives directly. Computers have made profound changes to the structure of physics. The physics community now actively pursues problems that were first thought to be too messy, such as strength and economics (called econophysics in this context). There might be a grain of truth to the view that physics has changed from being defined as the study of a certain class of problems to becoming a toolbox for solving various problems. If we were to define the fundamental difference in traditional versus statistical physics approaches, we'd see that researchers have traditionally approached the strength problem as perturbations on a homogeneous, disorderless problem. The statistical physics approach, on the other hand, takes the opposite limit as a starting point. The percolation problem, mentioned earlier in this article, can be formulated as an infinite disorder limit, meaning we treat the strength problem as perturbations away from the infinite-disorder limit.