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.

Citation

Nieves. (2019). Alternating Strain Regimes for Failure Propagation in Flexural Systems. Quarterly Journal of Mechanics and Applied Mathematics, 305 - 339. https://doi.org/10.1093/qjmam/hbz008

• 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