Plastic hinges as phase transitions in strain softening beams

Abstract

A jump between the upper yield point and lower yield point is well evident in strain driven tests on lowcarbon steel bars. However, in the constitutive equations commonly used to model the elastic-plastic flexure of beams this jump is usually neglected. Here, we show instead that such jump, albeit small, may drastically vary the structural response, because it renders the moment-curvature relationship of the beam strain-softening in type and with horizontal asymptotes. Because of this, with a process analogous to a phase transition within the solid state itself, strain may suddenly localize in the form of concentrated rotations of the beam axis, indeed forming a plastic hinge in the classical sense of limit analysis. Therefore, the formation of plastic hinges, usually indicated as an approximate or technical model, is now rigorously predicted by this approach. Experimental observations corroborate this finding.