Some Physical Concepts in Theories of Plastic Flow

Abstract

The mathematical formulation of any theory for the deformation of matter consists essentially in the development of differential equations relating the resistance developed by deforming forces to the relative displacements of differential elements and the successive time derivatives of these displacements. Such general formulations have been carried out for the elastic theory and for the theory of viscous flow, which are based on simple linear relations between the stress components and the strain components and their first time derivatives, respectively. For more complicated theories such general formulations are somewhat academic, as the resulting equations can only be solved for cases of flow in which a high degree of symmetry obtains, so that the equations and the boundary conditions reduce to comparatively simple forms. It is therefore sufficient to formulate any theory in terms general enough to include the cases of interest for which solutions can be obtained.