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arXiv · 0907.1426

Softening Gradient Plasticity: Analytical Study of Localization under Nonuniform Stress

Milan Jirasek·Jan Zeman·Jaroslav Vondrejc
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Abstract

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 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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Milan Jirasek, Jan Zeman, Jaroslav Vondrejc. 2009-07-09. Softening Gradient Plasticity: Analytical Study of Localization under Nonuniform Stress. https://doi.org/10.1615/intjmultcompeng.v8.i1.40

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