Numerical construction of deformation field in converging channel

This work proposes the computational method for the construction of the stress field in the deformation region in a converging channel. The stress components are assumed to satisfy Mohr-Coulomb yield criteria under plane strain condition. The governing equation for the model is the first-order partial differential equation, which is the stress equilibrium equations. The deformation region is made up of the union of adjacent elementary boundary value problem and solved numerically. The region is constructed by using Matlab, and it shows the formation of the two symmetrical deformation region at both upper and lower part of the converging channel. From the computation, we obtained the stress variables and the velocity distribution in the deformation region. The work rate for the corresponding velocity was calculated, then it is shown that the solutions are physically significant since the condition of the work rate is everywhere positive. This method is of great interest as it will bring about an increase in efficiency and hence improvement in industrial productivity, especially in designing granular flow device. The technique is also an alternative for the solution of the deformation problems as it is simple and more reliable. (paper)