A method of analysis for planar ideal plastic flows of anisotropic materials

The objective of the present paper is to provide an efficient method for finding steady planar ideal plastic flows of anisotropic materials. The method consists of determining two mappings between coordinate systems. One of these mappings is between principal lines-based and characteristics-based co...

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Bibliographic Details
Published in:Acta mechanica 2017-11, Vol.228 (11), p.3839-3846
Main Authors: Alexandrov, Sergei, Jeong, Woncheol
Format: Article
Language:English
Subjects:
Analysis
Anisotropy
Boundary value problems
Cartesian coordinates
Classical and Continuum Physics
Control
Dynamical Systems
Engineering
Engineering Thermodynamics
Heat and Mass Transfer
Integrals
Mapping
Methods
Original Paper
Plastics
Solid Mechanics
Theoretical and Applied Mechanics
Velocity
Vibration
Visualization
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Summary:The objective of the present paper is to provide an efficient method for finding steady planar ideal plastic flows of anisotropic materials. The method consists of determining two mappings between coordinate systems. One of these mappings is between principal lines-based and characteristics-based coordinate systems, and the other is between Cartesian- and characteristics-based coordinate systems. Thus, the mapping between the Cartesian- and principal lines-based coordinate systems is given in parametric form. It is shown that the boundary value problem of finding the mapping between the principal lines-based and characteristics-based coordinate systems can be reduced to the solution of a telegraph equation where two families of characteristics are curved and to the evaluation of ordinary integrals where one family of characteristics is straight. In either case, after solving this problem the problem of finding the mapping between the Cartesian- and characteristics- based coordinate systems can be reduced to the evaluation of ordinary integrals.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-017-1915-3