II.1 - The Modeling of Inelastic Compressibility and Incompressibility Using the Viscoplasticity Theory Based on Overstress (VBO)

Abstract

VBO is applied to metals and alloys at low and high homologous temperatures and has been extended to the modeling of solid polymers. This chapter introduces the isotropic small strain theory with and without inelastic incompressibility. A simplified version of VBO, which needs only five constants for the characterization of inelastic behavior, is discussed and applied to uniaxial, monotonic, and cyclic loading, as well as ratcheting of AISI 1026 steel at room temperature with good results. The VBO model is presented for isotropy, compressible and incompressible inelastic behavior, low and high homologous temperature for isothermal and variable temperature conditions. The model does not contain any strain measure and is written in terms of rates with the current configuration. The finite deformation version differs from the small strain version only by the objective stress and strain rates. These objective rates contain spins derived from the velocity gradient or its anti-symmetric part. The spins are zero in some motions. This is the case for the important state of uniaxial deformation.