SECTION 5.6 – Inelastic Compressible and Incompressible, Isotropic, Small Strain Viscoplasticity Theory Based on Overstress (VBO)

A tenet of materials science is that “the current behavior of a material is determined by its current state and the current loading conditions.” A properly designed specimen represents the material and serves as the integrator of all the micromechanisms. From these responses the continuum model has to be synthesized. It is clear that an experiment-based approach captures the physics of material behavior; after all, acting micromechanisms are deduced from similar, if not identical, tests. The aim of this chapter is to create an experiment-based, physical, small strain model that can be exercised like a real, servo-controlled testing machine with strain measurement on the gage section. A time integration program for a system of stiff, ordinary differential equations is the numerical testing machine. Viscoplasticity theory based on overstress (VBO) is used at low, high, and variable temperatures with one basic formulation. A static recovery term becomes negligible for low homologous temperature. Terms that are present for variable temperature equal zero when the temperature is constant. Creep and plasticity are not separately formulated. All material constants are allowed to vary with temperature.

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