Authors: B D Reddy
Publish Date: 2011/09/22
Volume: 23, Issue: 6, Pages: 551-
Abstract
Variational formulations are constructed for rateindependent problems in smalldeformation singlecrystal straingradient plasticity The framework based on that of Gurtin J Mech Phys Solids 50 5–32 2002 makes use of the flow rule expressed in terms of the dissipation function Provision is made for energetic and dissipative microstresses Both recoverable and nonrecoverable defect energies are incorporated into the variational framework The recoverable energies include those that depend smoothly on the slip gradients the Burgers tensor or on the dislocation densities Gurtin et al J Mech Phys Solids 551853–1878 2007 as well as an energy proposed by Ohno and Okumura J Mech Phys Solids 551879–1898 2007 which leads to excellent agreement with experimental results and which is positively homogeneous and therefore not differentiable at zero slip gradient Furthermore the variational formulation accommodates a nonrecoverable energy due to Ohno et al Int J Mod Phys B 225937–5942 2008 which is also positively homogeneous and a function of the accumulated dislocation density Conditions for the existence and uniqueness of solutions are established for the various examples of defect energy with or without the presence of hardening or slip resistance
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