https://doi.org/10.1140/epjp/s13360-024-05721-y
Regular Article
Nonlocal vibration of crack front particles entangled by phase transformation caused by fracture as shock-wave state
1
Department of Mechanical Engineering, Kitami Institute of Technology, 090-8507, Kitami, Hokkaido, Japan
2
, Kouencho 141-3, 090-0015, Kitami, Hokkaido, Japan
a kobayasi@mail.kitami-it.ac.jp, michiakikobayashi168@gmail.com
Received:
7
August
2024
Accepted:
1
October
2024
Published online:
2
November
2024
Based on the proposed crack opening criterion, the author theoretically derived and simulated the phase velocity and the strain at the crack tip under the fracture to be infinity physically caused by the optical mode of lattice vibration under wave number k = 0. Then, the phase information at the crack tip under the fracture is transferred instantaneously far away due to the phase velocity and wavelength being infinity and the separated particles at the crack front vibrate nonlocally under entanglement due to phase transformation caused by fracture. According to numerical results simulated by the mass–spring 2D model at the crack front under the fracture, the optical mode vibration at the crack front has been revealed. In this paper, to examine non-locality and entanglement conditions of the optical mode of lattice vibration, the local causality of lattice vibration is examined and it is deduced that acoustic mode of lattice vibration is under local causality; on the other hand, nonlocal vibration of optical mode of lattice vibration under the macroscopic scale is excited by the fracture. At wave number k = 0 under which both the phase velocity and the wavelength of the optical mode are infinity, the entanglement of optical mode of lattice vibration is established completely and is not dependent on locations, distance/space and time due to instantaneously simultaneous synchronization. This situation is realized between separated and entangled particles at the crack front under the fracture. However, incomplete entanglement between moving particles with mass is dependent on locations, distance/space and time due to delayed synchronization under the finite phase velocity and the finite wavelength.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
