A time integration procedure for plastic deformation in elastic-viscoplastic metals

A simple unconditionally stable numerical procedure for time integration of the flow rule for large plastic deformation of an elastic-viscoplastic metal is developed. Specific attention is focused on a unified set of constitutive equations which represents a generalization (for large deformation and thermomechanical response) of the Bodner-Partom model [6, 7]. An analytical solution is obtained for large deformation simple shear at constant shear rate. Numerical examples of simple shear, a corner test exhibiting the transition from uniaxial compression to shear, and simple tension are considered which demonstrate the stability and accuracy of the procedure. It is shown that the same procedure can be used for a rate insensitive metal characterized by a yield function as well as for a rate sensitive metal characterized by an overstress model. Finally, an appendix is provided which records the basic equations associated with the small deformation theory.

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