Analysis of dynamic failure of the discrete chain structure with non-local interactions

TL;DR

This paper investigates how non-local interactions in a chain of oscillators influence steady-state crack propagation, revealing changes in stability regions and solution structure through analytical and numerical methods.

Contribution

It introduces a model incorporating non-local interactions in a chain of oscillators and analyzes their impact on crack propagation using Wiener-Hopf techniques.

Findings

Non-local interactions alter the solution structure of crack propagation.

The stability region for crack motion is affected by non-local interactions.

Numerical results support the analytical findings.

Abstract

In the present work the steady-state crack propagation in a chain of oscillators with non-local interactions is considered. The interactions are modeled as linear springs while the crack is presented by the absence of extra springs. The problem is reduced to the Wiener-Hopf type and solution is presented in terms of inverse Fourier transform. It is shown that the non-local interactions may change the structure of the problem solution well-known from the classical local interactions formulation. In particular, it may change the range of the region of stable crack motion. The conclusions of the analysis are supported by numerical results. Namely, the observed phenomenon is partially clarified by evaluation of the structure profiles on the crack line ahead.