A mechanical model for the elastic–plastic behavior of metallic bars

Froli, Maurizio; Royer-Carfagni, Gianni

doi:10.1016/s0020-7683(99)00069-4

Cited by 26 publications

(18 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Indeed, such a jump is well evident in strain driven experimental tests [Froli and Royer-Carfagni 1999] and is responsible for the orderly formation of Lüder's bands [Froli and Royer-Carfagni 2000]. This jump is usually neglected in the elastic-plastic technical theories, but once it is considered, the moment-curvature relationship, deduced under the same hypotheses of the classical theories of beams, exhibits a strain-softening branch, while the associated flexural strain potential becomes nonconvex and with oblique asymptotes.…”

Section: Discussionmentioning

confidence: 92%

“…In fact, at the nanoscale, the stress drop can be attributed to the pinning of the dislocations (Peierls-Nabarro effect) due to the presence of solute atoms of carbons in the metallic lattice [Cottrell 1953]. It has been demonstrated [Froli and Royer-Carfagni 2000] that the consideration of such a jump is of crucial importance for the orderly formation, at the microscale, of slip (Lüder) bands in stretched bars of mild steel.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Plastic hinges as phase transitions in strain softening beams

Royer-Carfagni

Buratti

2007

JOMMS

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Discussionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Plastic hinges as phase transitions in strain softening beams

Royer-Carfagni

Buratti

2007

JOMMS

Self Cite

View full text Add to dashboard Cite

show abstract

“…The computational efficiency of the algorithm described in the previous sections was verified to the example, the results of which are known in literature (Froli and Royer-Carfagni, 2000). In the order to simulate experimental results, they refer to the test reported in their paper, where the specimen presented approximately…”

Section: Numerical Testmentioning

confidence: 85%

“…The phenomenon of discontinuous plastic deformation has been seriously considered from the beginning of the 19th Century up to today (Froli and Royer-Carfagni, 2000). The subject has been analyzed into two distinct ways.…”

Section: Introductionmentioning

confidence: 99%

Rheological–dynamical analogy: visco-elasto-plastic behavior of metallic bars

Milašinović

2004

International Journal of Solids and Structures

View full text Add to dashboard Cite

“…A possible explanation stems from the observation that the yield point of metals is greatly influenced by any stress concentration. There is a wealth of experimental evidence [19] that localized yielding produces a condition equivalent to a stress concentration at the boundary of the yielded portion, which can greatly influence [20] the behavior of the neighboring parts (nonlocal effect). The yielding of the first portion produces a chain reaction that produces the spreading of plastic deformation through the specimen similar to the cold drawing of polymers.…”

Section: Comparison With Experiments and Conclusionmentioning

confidence: 99%

From 3-D Nonlinear Elasticity Theory to 1-D Bars with Nonconvex Energy

Buonsanti

Royer-Carfagni

The Rational Spirit in Modern Continuum Mechanics

Self Cite

View full text Add to dashboard Cite

Abstract. This paper represents a first attempt to derive one-dimensional models with non-convex strain energy starting from "genuine" three-dimensional, nonlinear, compressible, elasticity theory. Following the usual method of obtaining beam theories, we show here for a constrained kinematics appropriate for long cylinders governed by a polyconvex, objective, stored energy function, that the bar model originally proposed by Ericksen [3] is obtainable but enriched by an additional term in the strain gradient. This term, characteristic of nonsimple grade-2 materials, penalizes interfacial energies and makes single-interface two-phase solutions preferred. The resulting model has been proposed by a number of authors to describe the phenomenon of necking and cold drawing in polymeric fibers and, here, we discuss its suitability to interpret also the elastic-plastic behavior of metallic tensile bars under monotone loading. (2000): 74A45, 74B20, 74G55, 74G65, 74N20. Mathematics Subject Classifications

show abstract

A mechanical model for the elastic–plastic behavior of metallic bars

Cited by 26 publications

References 11 publications

Plastic hinges as phase transitions in strain softening beams

Plastic hinges as phase transitions in strain softening beams

Rheological–dynamical analogy: visco-elasto-plastic behavior of metallic bars

From 3-D Nonlinear Elasticity Theory to 1-D Bars with Nonconvex Energy

Contact Info

Product

Resources

About