Prandtl-Reuss elastoplasticity: On-off switch and superposition formulae

Constitutive postulates for Prandtl-Reuss elastoplasticity are selected. Based on them, sufficient and necessary conditions for plastic irreversibility are found to be the yield condition and the straining condition. This is then analyzed and it is pointed out that Prandtl-Reuss elastoplasticity is nothing but a two-phase linear system with an on-off switch, which is operated in the pace of an intrinsic measure of plastic irreversibility. Then the temporally global concept of the switch-on time I, and the switch-off time r,and their determination and bound estimation is developed. Owing to the implicit linearity, superposition formulae for the stress response are discovered. As an example, the exact constitutive solutions for circular paths based on the superposition formulae are obtained and 1, and to,rare determined. 0 1997 Elsevier Science Ltd.