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ISSN Печать: 1543-1649
ISSN Онлайн: 1940-4352
Indexed in
Softening Gradient Plasticity: Analytical Study of Localization under Nonuniform Stress
Краткое описание
Localization of plastic strain induced by softening can be objectively described by a regularized plasticity model that postulates a dependence of the current yield stress on a nonlocal softening variable defined by a differential (gradient) expression. This paper presents analytical solutions of the one-dimensional localization problem under certain special nonuniform stress distributions. The one-dimensional problem can be interpreted as describing either a tensile bar with a variable cross section or a beam subjected to a nonuniform bending moment. Explicit as well as implicit gradient formulations are considered. The evolution of the plastic strain profile and the shape of the load-displacement diagram are investigated. It is shown that even if the local constitutive law exhibits softening right from the onset of yielding, the global load-displacement diagram has a hardening part. The interplay between the internal length scales characterizing the material and the geometry is discussed.
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Jirásek, M. and Rolshoven, S., Localization properties of strain-softening gradient plasticity models. Part II: Theories with gradients of internal variables. DOI: 10.1016/j.ijsolstr.2008.12.018
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Mühlhaus, H. B. and Aifantis, E. C., A variational principle for gradient plasticity. DOI: 10.1016/0020-7683(91)90004-Y
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Peerlings, R. H. J., de Borst, R., Brekelmans, W. A. M., and de Vree, J. H. P., Gradient-enhanced damage for quasi-brittle materials. DOI: 10.1002/(SICI)1097-0207(19961015)39:19<3391::AID-NME7>3.0.CO;2-D
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Peerlings, R. H. J., On the role of moving elastic-plastic boundaries in strain gradient plasticity. DOI: 10.1088/0965-0393/15/1/S10
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Pietruszczak, S. and Mróz, Z., Finite element analysis of deformation of strain-softening materials. DOI: 10.1002/nme.1620170303
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Strömberg, L. and Ristinmaa, M., FE-formulation of a nonlocal plasticity theory.
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Vermeer, P. A. and Brinkgreve, R. B. J., A new effective non-local strain measure for softening plasticity.
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Zbib, H. M. and Aifantis, E. C., On the localization and postlocalization behavior of plastic deformation.
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