A new computational strategy for analysing plastic deformation processes

Abstract

The paper describes a computer-based methodology for evaluating various strain and stress components within the body of a material undergoing plastic deformation. The strategy uses as input the grid distortion data, which provides the magnitudes of macroscopic particle velocities at discrete (nodal) points. To facilitate computation of the various strain-rate and strain components by explicit differentiation, B-spline functional relationships have been established for this data employing interpolating techniques. Numerical solutions obtained using this methodology have been compared with FEM predictions, which indicate that the results are in good agreement. Further, using plasticity theory, a set of partial differential equations have been established to describe the stress gradients induced due to materials processing. The mathematical formulations in the work are described only in polar coordinates, but the program VISIO can also handle the nodal displacements prescribed in rectangular coordinates too.