Towards simulation of elasto-plastic deformation: An investigation

Can the deformation of a solid body during plastic flow be assumed to be similar to that of fluids? Here we investigate the possibility of using a modified Navier-Stokes equation as the governing differential equation by including elastic resistance. We adopt the microscopic point of view to explain the material behaviour by laying special emphasis on strain localisation and tension instabilities. A spring and damper model is constructed to obtain approximate simulation of the material behaviour. Based upon the understanding developed from simulating simple tests, we re-formulate the field equation using resistances to change in volume and shape. The new field equation reduces to the Navier-Stokes equation in the fluid limit and Cauchy's equation in the solid limit. The viscosity and second viscosity of fluids are clearly defined. Bulk and shear modulii and solid damping determine the solid behaviour. Pressure disappears from the field equation and so there is no need to invoke the continuity equation. The four material parameters are determinable from simple measurments. This paper tries to capture the various steps of the investigation which lead to the final result.