# Alternating strain regimes for failure propagation in flexural systems

## TL;DR

This paper investigates steady-state fracture propagation in a discrete mass-beam structure under sinusoidal loading, combining analytical and numerical methods to identify fracture regimes and dynamic features.

## Contribution

It introduces an analytical model reducing the fracture problem to a Wiener-Hopf equation and analyzes steady-state fracture regimes in a discrete structure.

## Key findings

- Minimum wave energy needed for steady-state fracture identified
- Dynamic features of the structure during fracture characterized
- Transient analysis confirms steady-state regimes

## Abstract

We consider both analytical and numerical studies of a steady-state fracture process inside a discrete mass-beam structure, composed of periodically placed masses connected by Euler-Bernoulli beams. A fault inside the structure is assumed to propagate with a constant speed and this occurs as a result of the action of a remote sinusoidal, mechanical load. The established regime of fracture corresponds to the case of an alternating generalised strain regime. The model is reduced to a Wiener-Hopf equation and its solution is presented. We determine the minimum feeding wave energy required for the steady-state fracture process to occur. In addition, we identify the dynamic features of the structure during the steady-state fracture regime. A transient analysis of this problem is also presented, where the existence of steady-state fracture regimes, revealed by the analytical model, are verified and the associated transient features of this process are discussed.