Visco-Elastic Plate Motion after Its Breaking into Parts

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.

Automated summary

This paper studies the mathematical modeling of visco-elastic plate breaking and the consequent deflection of the plate. By using a simplified formulation, the authors model the plate as a thin visco-elastic plate with constant thickness and clamped edges. The plate deflection is caused by a gradually increasing aerodynamic pressure, and the plate breaks instantly when a modified fracture criterion is met. The motion of the plate parts after breaking is highly unsteady and dependent on the plate's viscous properties.