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International Journal for Multiscale Computational Engineering

Publication de 6  numéros par an

ISSN Imprimer: 1543-1649

ISSN En ligne: 1940-4352

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Softening Gradient Plasticity: Analytical Study of Localization under Nonuniform Stress

Volume 8, Numéro 1, 2010, pp. 37-60
DOI: 10.1615/IntJMultCompEng.v8.i1.40
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RÉSUMÉ

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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CITÉ PAR
  1. Challamel Noël, A variationally based nonlocal damage model to predict diffuse microcracking evolution, International Journal of Mechanical Sciences, 52, 12, 2010. Crossref

  2. Jirásek Milan, Rokoš Ondřej, Zeman Jan, Localization analysis of variationally based gradient plasticity model, International Journal of Solids and Structures, 50, 1, 2013. Crossref

  3. Polizzotto Castrenze, Surface effects, boundary conditions and evolution laws within second strain gradient plasticity, International Journal of Plasticity, 60, 2014. Crossref

  4. Rokoš Ondřej, Zeman Jan, Jirásek Milan, Localization analysis of an energy-based fourth-order gradient plasticity model, European Journal of Mechanics - A/Solids, 55, 2016. Crossref

  5. Mielke Alexander, Roubíček Tomàš, Applications in continuum mechanics and physics of solids, in Rate-Independent Systems, 193, 2015. Crossref

  6. Gerasimov Tymofiy, Römer Ulrich, Vondřejc Jaroslav, Matthies Hermann G., De Lorenzis Laura, Stochastic phase-field modeling of brittle fracture: Computing multiple crack patterns and their probabilities, Computer Methods in Applied Mechanics and Engineering, 372, 2020. Crossref

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