"1" . "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 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."@en . . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . "24"^^ . . . . . "Softening Gradient Plasticity: Analytical Study of Localization Under Nonuniform Stress" . "1543-1649" . . "000275277600004" . "plasticity; regularization; gradient theories; strain softening; strain localization"@en . "3"^^ . . "21110" . . "Vond\u0159ejc, Jaroslav" . . . "8" . "Jir\u00E1sek, Milan" . . "3"^^ . "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 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." . . "Softening Gradient Plasticity: Analytical Study of Localization Under Nonuniform Stress"@en . . . "[D34E2341CDB0]" . "Softening Gradient Plasticity: Analytical Study of Localization Under Nonuniform Stress"@en . "Softening Gradient Plasticity: Analytical Study of Localization Under Nonuniform Stress" . "288235" . "International Journal for Multiscale Computational Engineering" . "P(GA106/08/1508), Z(MSM6840770003)" . "Zeman, Jan" . "RIV/68407700:21110/10:00167269!RIV11-GA0-21110___" . "RIV/68407700:21110/10:00167269" . . . . . . . .