A Skew-Symmetric Plastic Potential Model for Material Processing Lagrangian Formulation

In manufacturing processes, precise processing of materials is crucial for producing high-quality products, and in metal forming and machining, accurate process design that considers plastic deformation is essential. The plastic potential theory is a popular approach for determining the rate of plastic flow, particularly within the framework of the Lagrangian formulation. This method is thermodynamically valid because the rate of plastic deformation adequately satisfies the dissipation inequality; however, its effect on the skew-symmetric plastic spin has not been considered directly, an issue which this paper particularly highlights. To account for plastic spin, which directly affects the distortion of the material axes, an additional constitutive equation is required. Consequently, the effect of skew-symmetric spin has been overlooked for convenience in plastic potential theory. This study introduces the theoretical structure of an asymmetric plastic potential function that models both the rate of plastic deformation and the rate of plastic spin using one constitutive equation in the Lagrangian formulation. The plastic potential function is derived from material dissipation, with its symmetric and asymmetric components governing the rates of plastic deformation and plastic spin, respectively. In simpler terms, the asymmetric plastic potential establishes the plastic velocity gradient, and not just the rate of plastic deformation. This study shows that the proposed method satisfies the dissipation inequality and theoretically discusses the completeness of the plastic potential theory through skew-symmetric potential modeling. Finally, it is shown that simulations with the proposed model effectively predict the observations of the evolution of material axes that the general plastic potential function cannot account for under uniaxial tension conditions.