Modeling the Elasto-Visco-Plastic Bending of Spatially Reinforced Plates Accounting for the Strain-Rate Sensitivity of Composition Components

Abstract

A version of the model of elasto-visco-plastic deformation is developed taking into account the strain-rate sensitivity. This model leads, as a special case, to the equations of the Prandtl-Reuss-Hill flow theory resolved for stress rates. This mechanical model is used in deriving the structural relations describing inelastic deformation of spatially reinforced composite media based on an algorithm of time steps. In addition, a mathematical model is constructed for elasto-visco-plastic bending behavior of reinforced plates when the possible weak resistance to transverse shear is taken into account in the framework of the traditional nonclassical Hambardzumyan theory and the geometric nonlinearity of the problem is given in the Karman approximation. The solution to the initial boundary value problem is based on an explicit numerical cross-type scheme. The bending inelastic dynamic deformation is investigated for plane and spatially reinforced fiberglass and metal composite rectangular plates under the action of a load caused by an air blast wave. It is shown that the neglect of the strain-rate sensitivity of the composition components most commonly leads to an overestimation of the calculated deflections and the strain state characteristics of these components. It is demonstrated that for relatively thick structures the replacement of the flat reinforcement structure by the spatial structure implies a decrease in the intensity of the binder deformation by tens of percent as well as to a decrease in the plate deflections (it is insignificant in the case of metal composite structures and is on the order of tens of percent in the case of fiberglass plates). For relatively thin structures the replacement of the plane reinforcement structure by the spatial reinforcement structure does not result in a decrease in their flexibility in the transverse direction and in a decrease of the strain state characteristics of the composition components.