Oscar Lopez-Pamies (Illinois) - The Fracture of Everything (Brittle) With Applications to the Indentation of Glass and the Stretching of Rubber

In this talk, I will begin by summarizing the slew of existing macroscopic experimental results amassed over the past century on how nominally elastic brittle materials nucleate and propagate cracks when subjected to mechanical loads applied quasistatically. When viewed collectively, the experiments make it plain that there are three basic ingredients that any attempt at a comprehensive macroscopic theory of deformation and fracture ought to account for: (i) the elasticity of the material, (ii) its strength at large, and (iii) its fracture energy. 

Having pinpointed to the basic ingredients required for a complete theory, I will then present one such theory, regularized, of phase-field type. The theory can be viewed as a natural generalization of the phase-field approximation of the celebrated variational theory of brittle fracture of Francfort and Marigo (1993) to account for the material strength at large. This is accomplished by the addition of an external driving force — which physically represents the macroscopic manifestation of the presence of inherent microscopic defects in the material — in the equation governing the evolution of the phase field.

In the latter part of the presentation, I will illustrate the descriptive and predictive capabilities of the theory via simulations of two famous problems: the indentation of glass plates with flat-ended cylindrical indenters and the stretching of poker-chip rubber specimens. I will close with a number of remarks on the implications of the results for fracture in materials at large, not just elastic.