Abstract : 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.
Bio-sketch : Oscar Lopez-Pamies is the Colonel Harry F. & Frankie M. Lovell Professor in the Department of Civil and Environmental Engineering at the University of Illinois Urbana-Champaign, which he joined in 2011. He received his B.A. degree in Mathematics and B.S. and M.S. degrees in Mechanical Engineering from the University of Maryland Baltimore County in 2001 and 2002, and his Ph.D. degrees in Applied Mechanics from the University of Pennsylvania and Ecole Polytechnique (France) in 2006. His research focuses on the development of mathematical theories and associated numerical methods to describe, explain, and predict the mechanical and physical behavior, stability, and failure of highly deformable heterogeneous solids. He is the recipient of a number of academic honors, including the Young Scientist Prize from the European Mechanics Society in 2009, the NSF CAREER award in 2011, the Journal of Applied Mechanics award in 2014, and the Young Investigator Medal from the Society of Engineering Science in 2017.
