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Main Title: Thin‐layer inertial effects in plasticity and dynamics in the Prandtl problem
Author(s): Georgievskii, Dmitri V.
Müller, Wolfgang H.
Abali, Bilen Emek
Type: Article
Language Code: en
Abstract: Especially in metal forming, large plastic deformation occurs in thin plates. The problem of compressing dies is analyzed to evaluate the spreading of a thin layer in between. The velocity of dies is a given function in time so that the kinematics of the process is known. This problem can be considered as a generalization of the classical Prandtl problem by taking inertial effects into account and introducing dimensionless parameters as internal variables depending on time. The first parameter is purely geometric corresponding to the thin‐layer approximation; the second and the third parameters are dimensionless velocity and acceleration during the dies getting pressed. We use singular asymptotic expansions of unknown functions and study how these parameters vary preceding the dies of moment. Depending on this relation, the dynamic corrections to the quasistatic solution is a part of various terms of the asymptotic series. The corresponding analytical investigation both for general case and for particular typical regimes of plates motion is carried out.
Issue Date: 23-Oct-2019
Date Available: 13-Feb-2020
DDC Class: 510 Mathematik
530 Physik
Subject(s): analytical mechanics
inertial effects
thin layers
Sponsor/Funder: TU Berlin, Open-Access-Mittel - 2019
Journal Title: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Publisher: Wiley
Publisher Place: Berlin
Volume: 99
Issue: 12
Article Number: e201900184
Publisher DOI: 10.1002/zamm.201900184
EISSN: 1521-4001
ISSN: 0044-2267
Appears in Collections:FG Kontinuumsmechanik und Materialtheorie » Publications

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