An Einstein Model of Brittle Crack Propagation
Abstract
We propose a minimal nonlinear model of brittle crack propagation by considering only the motion of the crack-tip atom. The model captures many essential features of steady-state crack velocity and is in excellent quantitative agreement with many-body dynamical simulations. The model exhibits lattice-trapping. For loads just above this, the crack velocity rises sharply, reaching a limiting value well below that predicted by elastic continuum theory. We trace the origin of the low limiting velocity to the anharmonicity of the potential well experienced by the crack-tip atom.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.