ON THE REPLACEMENT OF MATERIAL-TIME DERIVATIVE TO COROTATIONAL RATE OF YIELD FUNCTION: MATHEMATICAL PROOF

ABSTRACT: Constitutive equations have to be formulated in an indifferent form independent of the frame (i.e. coordinate systems) by which they are described or so as to be independent of the superposition of rigid body rotation. This fact is required by the principle of material-frame indifference (Oldroyd, 1950) and is attained conveniently by describing rate variables in terms of rate tensors with objectivity in constitutive equations in rate form. A plastic strain rate is derived by substituting the plastic flow rule into the consistency condition given as the material-time derivative of yield condition. In this note the mathematical process demonstrates the fact that the rate variables involved in the material-time derivative of yield function can be directly replaced with their objective rate tensors. Here, the yield function involves arbitrary tensors, whilst the special case that the yield function involves only a single tensor or second-order tensors has been discussed in the past.

Key words: constitutive equation, (corotational rate), elastoplasticity, (material-time derivative ), (objectivity), yield (IGC: D6/E2)