Abstract
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.
Highlights
In the case of rigid perfectly plastic solids, several efficient methods that utilize this or that property of special coordinate systems are used for solving plane strain boundary value problems
In the case of the pyramid yield criterion used for powder and porous materials [5] plane strain deformation occurs at an edge of the yield surface
On the assumption of plane strain conditions the system of equations comprising the piramyd yield criterion (1) and the equilibrium equations has been solved in a curvilinear orthogonal coordinate system in which the coordinate curves coincide with trajectories of the principal stress directions
Summary
In the case of rigid perfectly plastic solids, several efficient methods that utilize this or that property of special coordinate systems are used for solving plane strain boundary value problems. An important relation between the scale factors of a principal line coordinate system has been derived in [3] Using this property it is possible to develop an efficient method of calculating principal stress trajectories. This has been demonstrated in [4] where the Mohr-Coulomb yield criterion has been adopted. In the case of the pyramid yield criterion used for powder and porous materials [5] plane strain deformation occurs at an edge of the yield surface. The method of Mikhlin’s coordinates has been generalized on the pyramid yield criterion in [6]. A principal line theory of axially symmetric plastic deformation has been developed in [9] for the face regime of the Tresca yield criterion and its associated flow rule
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
