# Visco-elastic plate motion after its breaking into parts

Korobkin, Alexander ORCID: https://orcid.org/0000-0003-3605-8450 and Khabakhpasheva, Tatiana ORCID: https://orcid.org/0000-0003-4058-0508 (2022) Visco-elastic plate motion after its breaking into parts. Journal of Marine Science and Engineering, 10 (6). ISSN 2077-1312

## Abstract

Mathematical modelling of visco-elastic plate breaking and consequent deflection of the plate are studied using the simplified formulation. The plate is modelled as a thin visco-elastic plate of constant thickness. The edges of the plate are clamped. The plate deflection is caused by a uniform aerodynamic pressure, which slowly increases in time. The plate deflection before breaking is approximated as quasi-static. The plate breaks instantly then and there, when and where the modified fracture criterion by Petrov and Morozov is achieved. Both the deflections and velocities of the plate before and after breaking are assumed equal.The motion of the plate parts after breaking are highly unsteady and dependent on the viscous properties of the plate. If the viscosity of the plate material is negligible compared with the elastic characteristics of the plate, then the velocity of the plate deflection is discontinuous at the time instant of the plate breaking. This feature of the plate motion after its breaking should be taken into account in interpretation of the numerical results within the linearised model of plate deflection with sudden breaking. It is shown that the plate can break in a cascade way. Each part after the first breaking breaks again. The configuration studied in this paper is specially tailored to highlight the behaviour of the numerical solutions of the plate breaking problems in applications.

Item Type: Article Funding Information: This work was supported by the NICOP research grant “Vertical penetration of an object through broken ice and floating ice plate” N62909-17-1-2128. elastic plate fracture,fluid structure interaction,initial stage,civil and structural engineering,water science and technology,ocean engineering ,/dk/atira/pure/subjectarea/asjc/2200/2205 Faculty of Science > School of Mathematics Faculty of Science > Research Groups > Fluid and Solid Mechanics http://www.scopus.com/inward/record.url?... LivePure Connector 04 Mar 2024 18:35 17 Jul 2024 01:45 https://ueaeprints.uea.ac.uk/id/eprint/94517 10.3390/jmse10060833