Geometry of principal stress trajectories for a Mohr‐Coulomb material under plane strain

Abstract

In the mechanics of granular and other materials the system of equations comprising the Mohr‐Coulomb yield criterion together with the stress equilibrium equations under plane strain conditions forms a statically determinate system. The results presented here for this system are consequently independent of any flow rule that may be chosen to calculate the deformation and also independent of whether elastic strains are included. 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 constructed relative to this coordinate system. A simple relation connecting the two scale factors for the coordinate curves is derived. In the special case that the angle of internal friction vanishes, this relation reduces to that already available for the Tresca yield criterion. A simple example is presented to illustrate the general solution. Finally, a boundary value problem for the region adjacent to an external boundary which coincides with a principal stress trajectory is formulated and its solution is outlined.

Stress-Strain State of a Plastic Layer under Compression by Two Rigid Parallel Rough Plates

“…Сondition (1) has a limited application. Nevertheless, there are meaningful papers [7][8][9][10][11], using, together with numerical methods, the condition (1). Hypotheses of a deformation character is the hypothesis of plane sections (HPS) [12][13][14][15][16] ( ) ( )…”

“…After substituting the expression for Y from ( 11) into (10), we obtain an analytic expression to calculate the shear stresses in the part of the layer under load:…”

A Method of Calculating Principal Stress Trajectories in Powder and Porous Materials Obeying a Piece-wise Linear Yield Criterion

“…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. The material model used in [3] is obtained as a special case.…”

Geometry of principal stress trajectories for piece‐wise linear yield criteria under axial symmetry

“…It is worthy of note that even if a boundary value problem is not statically determinate (i.e., the solution of stress equations cannot be found without using velocity boundary conditions), the stress equations constitute a closed form system ( i.e., the number of stress equations is equal to the number of unknown stress components). The main result obtained in [1] has been extended to the Mohr-Coulomb yield criterion in [2] and quite a general piece-wise linear yield criterion in [3]. In [3], a method for calculating the principal lines coordinate system based on the theory of characteristics has been developed.…”

“…In [3], a method for calculating the principal lines coordinate system based on the theory of characteristics has been developed. The method can be used in conjunction with the main result obtained in [1] and [2]. A general two -dimensional stress analysis of a hyperbolic system of equations comprising the equilibrium equation and quite a ge neral yield criterion has This article is protected by copyright.…”