MATEC Web Conf.
Volume 220, 20182018 The 2nd International Conference on Mechanical, System and Control Engineering (ICMSC 2018)
|Number of page(s)||4|
|Section||Functional Material Design and Modeling|
|Published online||29 October 2018|
A Method of Calculating Principal Stress Trajectories in Powder and Porous Materials Obeying a Piece-wise Linear Yield Criterion
1 School of Mechanical Engineering and Automation, Beihang University, Beijing, China
2 Laboratory of Mechanics of Technological Processes, Ishlinsky Institute for Problems in Mechanics RAS, Moscow, Russia
3 Metal Forming Laboratory, IIT Bombay, Mumbai, India
The present paper deals with the system of equations comprising the pyramid yield criterion together with the stress equilibrium equations under plane strain conditions. The stress equilibrium equations are written relative to a coordinate system in which the coordinate curves coincide with the trajectories of the principal stress directions. The general solution of the system is found giving a relation connecting the two scale factors for the coordinate curves. This relation is used for developing a method for finding the mapping between the principal lines and Cartesian coordinates with the use of a solution of a hyperbolic system of equations. In particular, the mapping between the principal lines and Cartesian coordinates is given in parametric form with the characteristic coordinates as parameters.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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