A generalized theory of plasticity

Abstract

The classical incremental theory of plasticity is not able to predict plastic strain accumulation during cycling loading. This because plastic deformation may occur only during loading conditions and when the stress point lies on the yield surface F. On the other hand, F remains fixed in the stress space durinf unloading conditions, so thar successice loading does not produce any plastic deformation until the stress point does not reach again F. this work presents a feneralizarion of the classical theory, which allows to describe plastic strain accumulation during cyclic loading. This obtained postulatinf that F follows always the stress point. Moreover, it is assumed the existence of a surface ${\textstyle {\bar {F}}}$, which bounds always F and of an elastic surface Failed to parse (unknown function "\wildehat"): {\textstyle \wildehat{F}} , which bounds the stress states at which only elastic strain mat occur. In the limit case Failed to parse (unknown function "\wildehat"): {\textstyle \wildehat{F} \equiv \bar{F}} F=F the presented generalized theory recovers the classical one.