Alternating Strain Regimes for Failure Propagation in Flexural Systems

Nieves

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.

• Acceptance Date: Mar 16, 2019
• Publication Date: May 13, 2019
• Journal: The Quarterly Journal of Mechanics and Applied Mathematics
• Print ISSN: 0033-5614
• Publisher: Oxford University Press
• Pages: 305 - 339
• DOI: https://doi.org/10.1093/qjmam/hbz008
• Keywords: Discrete periodic media, mass-beam structures, fracture, Wiener-Hopf technique, numerical simulations.
• Publisher URL: https://doi.org/10.1093/qjmam/hbz008