Planar 2-D Cracks And Inclusions In Elastic Media

TL;DR

This paper establishes a direct correspondence between electrical fuse network models and elastic fracture problems, demonstrating how discrete models approximate the continuous elastic media in fracture analysis.

Contribution

The paper explicitly links electrical analogues to elastic fracture problems and proves the convergence of fuse network models to their continuum elastic limits.

Findings

Established the analogy between fuse networks and elastic fracture.

Proved the convergence of discrete fuse models to continuum elastic media.

Clarified the relationship between discrete and continuous fracture models.

Abstract

Electrical analogues of fracture, such as the fuse network model, are widely studied. However, the "analogy" between the electrical problem and the elastic problem is rarely established explicitly. Further, the fuse network is a discrete approximation to the continuous problem of fracture. It is rarely, if ever, shown that the discrete approximation indeed approaches its continuum limit. We establish both of these correspondences directly.