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Plastic hinges as
phase transitions in strain softening beams
Gianni Royer-Carfagni and Giovanni Buratti |
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Vol. 2 (2007), No. 9, 1677–1699
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Abstract |
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A jump between the upper yield point and lower yield point is well evident in strain driven tests on low-carbon 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. |
Keywords
limit analysis, phase transition, strain localization,
plastic hinge, nonconvex minimization, holonomic plasticity
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Milestones
Received: 19 July 2006
Accepted: 13 February 2007
Published: 1 November 2007
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Authors |
| Gianni Royer-Carfagni | |
| Dipartimento di Ingegneria Civile,
dell’Ambiente, del Territorio e Architettura Università di Parma Parco Area delle Scienze 181/A I 43100 Parma Italy |
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| Giovanni Buratti | |
| I.T.C.G. Campedelli Castelnuovo di Garfagnana Lucca Italy |
Dipartimento di Ingegneria
Strutturale Università di Pisa 56126 Pisa Italy |
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