Abstract: Recent experiments, analogous to the classical experiments by Gent and collaborators but carried out at higher spatiotemporal resolution (of 1 micron in space and 60 ms in time), have provided a complete qualitative picture of the nucleation and the ensuing growth and interaction of internal cavities/cracks in elastomers subjected to externally applied quasi-static mechanical loads. Remarkably, the experiments have also revealed that internally nucleated cracks in elastomers can completely heal, even when they have grown to be several tens of micrometers in length scale.
In this talk, I will begin by presenting a continuum field theory seemingly capable to explain, describe, and predict all of the classical and recent experimental observations: from the nucleation of cavities/cracks, to their growth to micro-cracks, to their continued growth to macro-cracks, to the remarkable healing of some of the cracks. The theory rests on two central ideas. The first one is to view elastomers as solids capable to undergo finite deformations and capable also to phase transition to another solid of vanishingly small stiffness: whereas the forward phase transition serves to characterize the nucleation and propagation of fracture, the reverse phase transition characterizes the healing. The second central idea is to take the phase transition to be driven by the competition between a combination of strain energy and stress concentration in the bulk and surface energy on the created/healed new surfaces in the elastomer. In the second part of the talk, I will present a numerical implementation of the theory capable of efficiently dealing with large deformations, the typical near incompressibility of elastomers, and the large changes in the deformation field that can ensue locally in space and time from the nucleation of fracture.
Biosketch: Oscar Lopez-Pamies received his B.S. 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 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.