Abstract
It is emphasized that the sinusoidal response of the shear stress τ to large shear strain γ in a simple shear is not unreasonable at least in a mathematical sense (although it has long been considered unreasonable), and is dependent on the material property. Also it is found that the up-dated form of the constitutive equation is not necessarily equivalent to its original one except when the current rates of stress and strain are completely independent of the deformation state and history in a tensorial sense, which are commonly used unconditionally in the numerical deformation analysis by the incremental method. A new plastic constitutive equation is proposed which involves a new material constant ρ with 0≦ρ≦1. It reduces to the so-called J2-flow theory for ρ=0, and resembles the deformation theory for ρ=1. Its stress response to simple shear is discussed with various values of ρ, and the well-known axial extension of a cylinder subjected to torsion is explained using an appropriate value of ρ. The spin to be used in the constitutive equation and the evolution equation of thee internal variables are also discussed.
