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A Refined Model of Viscoelastic-Plastic Deformation of Flexible Plates with Spatial Reinforcement Structures

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Abstract

A refined model of viscoelastic-plastic deformation of flexible plates with spatial reinforcement structures has been developed. Strains of the composition materials are assumed to be small and decomposed into plastic and viscoelastic components. Instantaneous plastic deformation of these materials is described by the flow theory with isotropic hardening. Viscoelastic deformation obeys the governing equation of a linear model of a five-constant body. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The possible weak resistance of the composite plates to lateral shear is modeled within the refined theory of bending, which makes it possible to determine (with varying degrees of accuracy) the displacements of plate points and the stress–strain state in the components of the composition. In the first approximation, relations corresponding to the conventional nonclassical Reddy theory follow from the obtained equations and boundary conditions. A numerical solution to the formulated initial-boundary-value problem is sought using an explicit “cross-type” scheme. The viscoelastic-plastic dynamic deformation of rectangular, relatively thin fiberglass plastic plates under explosive-type load is investigated. The plates have a conventional planar-cross (orthogonal) or spatial reinforcement structure. It is shown that, even in the case of relatively thin composite plates, the Reddy theory cannot be used for adequate calculation of their dynamic viscoelastic-plastic deformation. It is demonstrated that the value and shape of residual deflections depend not only on the structural reinforcement but also on the viscoelastic characteristics of the materials of composition components. It is found that a composite plate subjected to dynamic inelastic deformation may acquire a corrugated residual shape with longitudinally oriented folds. It is shown that, even for a relatively thin plate, replacement of the planar-cross reinforcement structure with a spatial structure decreases significantly the residual deflection and intensity of residual deformation in both binder material and some fiber families. For relatively thick plates, the effect of this replacement of reinforcing structures is even more pronounced.

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Funding

This work was supported by the Program of Fundamental Research of State Academies of Sciences for 2017–2020 (project no. 23.4.1: “Mechanics of Deformation and Destruction of Materials and Media under Mechanical Loads, in Physical Fields, and in Chemically Active Media”).

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  1. Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, 600390, Novosibirsk, Russia

    A. P. Yankovskii

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Translated by Yu. Sin’kov

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Yankovskii, A.P. A Refined Model of Viscoelastic-Plastic Deformation of Flexible Plates with Spatial Reinforcement Structures. J Appl Mech Tech Phy 62, 1045–1062 (2021). https://doi.org/10.1134/S0021894421070208

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