A Strain-Rate Gradient Theory of Plasticity and its Comparison with Strain Gradient Theories

Gradient theories of plasticity play an important role in the description of inelastic behavior of materials. Usually, these theories involve space derivatives of stress or strain. On the other hand, conventional theories of plasticity can be divided into two groups, flow and deformation theories. Each of these groups has its own area of applications. The main conceptual difference between the theories belonging to the different groups is that the primary kinematics variables in deformation theories are displacements (or strains) whereas in flow theories velocities (or strain rates). Therefore, it is of interest to propose a gradient theory of plasticity involving space derivatives of a measure of strain rate (strain-rate gradient theory of plasticity) and to compare qualitative behavior of solutions for the strain-rate gradient theory of plasticity and an existing strain gradient theory of plasticity. One possible strain-rate gradient theory of plasticity is proposed in the present paper. The equivalent strain rate (second invariant of the strain rate tensor) is used as a measure of strain rate. The Laplacian operator is adopted to introduce the gradient term. An analytic solution for expansion of a hollow sphere is given for two strain-rate gradient theories of plasticity and one strain gradient theory. Comparison of the solutions shows that some qualitative features of the solutions for the strain-rate gradient theories are in better agreement with general physical expectations than those for the strain gradient theory.