Return Mapping for Creep and Plasticity Split

VÍCTOR FACHINOTTI; ALEJANDRO ALBANESI; ALBERTO CARDONA

San Pablo

Congreso; 10th World Congress on Computational Mechanics WCCM 2012; 2012

Within the range of validity of the small strain theory, the strain is additively decomposed in an elastic or reversible strain and an inelastic or irreversible strain. The inelastic strain consists of a plastic component quickly developed under loading, and a viscous or creep component that develops slowly under loading. Most frequently, both components are assumed to develop simultaneously following a unique flow rule for the whole inelastic strain according to the Bingham-Norton rheological model, which neglects creep recovery. Under experimental evidence of considerable creep recovery, instantaneous plastic strain and slow creep evolve according their own flow rules. Unlike the case Bingham-Norton models are used, it is no longer possible to define a trial stress state from which it can be determined whether the plastic strain has increased or not under a given load increment. We introduce a new “non-plastic” trial state, which differs from the classical elastic trial state (Simo and Hughes, Computational Inelasticity, Springer-Verlag, 1998) since creep increment is now allowed. In order to explicit the “non-plastic” trial state, the creep flow rule, generally nonlinear, is solved. From the “non-plastic” trial state, two alternatives can be derived: (i) no plastic increment has been produced (in such a case, the trial state is actually the solution); (ii) there must be plastic increment, and therefore the stress cannot exceed the yield stress. In the last case, the creep flow rule is supplemented by the plastic consistency condition, giving rise to a system of non-linear scalar equations, to be solved for determining the actual plasticand creep increment under the given load.