Mathematical modeling of the growth of crack pairs: The En-Passant problem
Year: 2014
Type: preprint
Abstract: . The problem of predicting the growth of a system of cracks, each crack influenc-ing the growth of the others, arises in multiple fields. We develop an analytical framework toward this aim, which focuses on modeling the En-Passant crack growth problem, in which a pair of initially parallel, offset cracks propagate nontrivially under far-field opening stress. We utilize boundary integral methods of linear elasticity, Linear Elastic Fracture Mechan-ics, and common crack opening criteria to produce a mathematical model for En-Passant crack paths. This integral system is reduced under a hierarchy of approximations, producing three methods of increasing simplicity for computing En-Passant crack paths. The last such method is a major highlight of this work, using an asymptotic matching argument to predict crack paths based on superposition of simple, single-crack fields. Within the correspond-ing limits of the three methods, all three are shown to agree with each other. We provide comparisons to exact results to verify certain approximation steps.
Source: arXiv (Cornell University)
Authors: R. Ghelichi, Ken Kamrin
Language: English
Subfield: Mechanics of Materials
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2898631018