A new theory of viscoplasticity is described that models yielding as a random phenomenon. A circle on the deviatoric stress plane represents the intensity of yielding with the radius equal to the random yielding microstress. This random model does not utilize a yield surface; yielding intensity is quantified by expected values defined in the deviatoric stress plane. The circle in the deviatoric stress plane with a random radius is a simple way to model multi-axial loading. Approximations for stress, strain energy density, and plastic strain energy density are used to improve the computational efficiency of parameter selection and to quantify the flow criterion. The exact state equations are derived, which can be manipulated to describe a wide variety of loading conditions for a broad temperature range. Reversed loading, stress relaxation, creep, and nonproportional loading are all natural properties of the model, which require little additional elaboration. Material properties were specified for five metals, three at room temperature and two over a wide temperature range.

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