Constitutive Relations for Generalized Loadings

A multisurface approach in stress space is adopted as the most general means of describing incrementally the plastic flow phenomena. Thee inner surface is the yield surface and the outer one is the bounding surface. All other surfaces are intermediate. The size of the surfaces may change in a congruent manner due to changes in the state variables. The surfaces can only translate. For plastic flow the two key parameters are the plastic strain at current time, and an increment in plastic strain from the current time to some future time for the case of monotonic outward loading. The locations of the center of a surface is a function of the preceding parameters. The examples given in the paper are for mild steel having a characteristic plateau and strain-hardening ranges. The proper balance between the influence of isotropic hardening compared to the kinematic one is achieved by using a variable weighing function.