 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| D.V. Georgievskii, "Thin-Layer Asymptotics in the Generalized Prandtl Problem for an Inhomogeneously Thick Plastic Material," Mech. Solids. 57 (8), 2050-2057 (2022) |
| Year |
2022 |
Volume |
57 |
Number |
8 |
Pages |
2050-2057 |
| DOI |
10.3103/S0025654422080143 |
| Title |
Thin-Layer Asymptotics in the Generalized Prandtl Problem for an Inhomogeneously Thick Plastic Material |
| Author(s) |
D.V. Georgievskii (Moscow State University, Moscow, Russia; Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia; Moscow Center for Fundamental and Applied Ìathematics, Moscow, Russia, georgiev@mech.math.msu.su) |
| Abstract |
The generalized Prandtl boundary value problem is considered, which simulates a quasistatic technological compression process in one direction and rapid spreading in another for a thin
incompressible perfectly rigid plastic layer (a plane strain state) corresponding to the Mises–Hencky
plasticity criterion with a yield stress variable in thickness. Stratification can be either continuous or
piecewise constant. In the latter case, the problem simulates the pressing of layered plastic composites
(laminates, “sandwiches”) and precisely bringing them to the desired thickness. On the basis of thinlayer singular asymptotics for a small geometric parameter, an approximate solution for kinematic and
force quantities is found using the asymptotic integration method developed in this study. The applicability of the quasistatic approach to various time ranges of the compression process is discussed. |
| Keywords |
perfect rigid plastic material, the Prandtl problem, thin-layered asymptotics, quasistatics, inhomogeneity, stratification, layered composite, sandwich, Euler number |
| Received |
20 April 2022 | Revised |
11 May 2022 | Accepted |
20 May 2022 |
| Link to Fulltext |
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