A Finite Deformation Theory of Viscoplasticity Based on Overstress: Part I—Constitutive Equations

The viscoplasticity theory based on overstress (VBO) is extended to finite deformation (FVBO). Yield surfaces and loading/unloading conditions are not part of this theory which represents creep, relaxation, and rate sensitivity in a “unified” way. Additive decomposition of the rate of deformation into the elastic and the inelastic parts is assumed. For the elastic part, the hypoelastic relation is used. For the inelastic part, the flow law of VBO is augmented by a term quadratic in the overstress together with a modified Jaumann stress rate which jointly or separately allow the modeling of second-order effects.