RT Journal Article
ID 719684a20f384669
A1 Jirasek, Milan
A1 Zeman, Jan
A1 Vondrejc, Jaroslav
T1 Softening Gradient Plasticity: Analytical Study of Localization under Nonuniform Stress
JF International Journal for Multiscale Computational Engineering
JO JMC
YR 2010
FD 2009-09-22
VO 8
IS 1
SP 37
OP 60
K1 plasticity
K1 regularization
K1 gradient theories
K1 strain softening
K1 strain localization
AB 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.
PB Begell House
LK https://www.dl.begellhouse.com/journals/61fd1b191cf7e96f,771f054c69c4607e,719684a20f384669.html