Brittle Fracture of Dissipative Solids

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

Because of its pervasiveness and high-stakes impact on the mechanical performance of structures made of inorganic and live matter alike, such as bridges, airplanes, bones, and ligaments, fractures have attracted the attention of humans, researchers and laymen alike, for centuries. Arguably, it is in the past 25 years of this long and rich history that most progress has been made in the quest for a complete mathematical formulation of fractures. This has been made possible by a pivotal idea, to wit, the casting of the phenomenon of fracture as a competition between energies: the energy required to deform the structure and the energy required to create a crack in the structure. Critically, this progress has been restricted to the elementary case of brittle fracture in elastic solids, that is, materials that respond in one of two ways to mechanical forces: they either deform elastically or create new surface, i.e., they fracture. Yet, while within certain restricted conditions some materials may be safely idealized as brittle elastic solids, as in the case of glass at room temperature, all materials dissipate energy when they deform, primarily by viscous or plastic deformation, or both, as for rubber and aluminum. In this context, based on a universal energy competition recently discovered by the investigator, this project aims to develop a rigorous mathematical formulation to describe fracture in dissipative solids at large. The project will provide interdisciplinary research training opportunities for graduate students. The project has three main objectives: 1) to develop a mathematically well-posed time-discrete formulation of brittle fracture evolution in a large class of dissipative solids subjected to isothermal quasistatic mechanical loading; 2) to develop a phase-field regularization of the time-discrete formulation and establish its convergence to the sharp limit; and 3) to numerically implement the developed phase-field formulation and validate its predictions against representative experiments on different types of solids. From a fundamental standpoint, the project seeks to provide a first step towards a mathematically well-posed universal formulation of fractures in any type of solid subjected to quasistatic mechanical loading. In other words, to provide a first step in establishing that the so-called brittle Griffith fracture is a universal description of fracture in any type of solid. From an applications standpoint, a tractable computational tool will be developed with the capability to describe, explain, and predict the nucleation of a fracture from large pre-existing cracks, as well as the propagation of fractures in structures made of a large class of dissipative solids under arbitrary quasistatic loading. Such a general quantitative tool would provide exceptional insight into a broad spectrum of phenomena dominated by fracture. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.