Variational constitutive updates for strain gradient isotropic plasticity

In the past decades, various strain gradient isotropic plasticity theories have been developed to describe the size-dependence plastic deformation mechanisms observed experimentally in micron-indentation, torsion, bending and thin-film bulge tests in metallic materials. Strain gradient plasticity theories also constitute a convenient device to introduce ellipticity in the differential equations governing plastic deformation in the presence of softening. The main challenge to the numerical formulations is that the effective plastic strain, a local internal variable in the classic isotropic plasticity theory, is now governed by the partial differential equation which includes spatial derivatives. Most of the current numerical formulations are based on Aifantis' one-parameter model with a Laplacian term [Aifantis and Muhlhaus, ijss, 28:845-857, 1991]. As indicated in the paper [Fleck and Hutchinson, jmps, 49:2245-2271, 2001], one parameter is not sufficient to match the experimental data. Therefore a robust and efficient computational framework that can deal with more parameters is still in need. In this thesis, a numerical formulation based on the framework of variational constitutive updates is presented to solve the initial boundary value problem in strain gradient isotropic plasticity. One advantage of this approach compared to the mixed methods is that it avoids the need to solve for both the displacement and the effective plastic strain fields simultaneously. Another advantage of this approach is, as has been amply established for many other material models, that the solution of the problem follows a minimum principle, thus providing a convenient basis for error estimation and adaptive remeshing.

Department dc:contributor.department

Massachusetts Institute of Technology. Computation for Design and Optimization Program.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2009

Author dc:creator

• Qiao, Lei, Ph. D. Massachusetts Institute of Technology

Advisor dc:contributor.advisor

• Raúl A. Radovitzky.

• Computation for Design and Optimization Program.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/55079

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/55079