Well-posedness of a model of strain gradient plasticity for plastically irrotational materials

Reddy, B. D., Ebobisse, F. and McBride, A. (2008) Well-posedness of a model of strain gradient plasticity for plastically irrotational materials. International Journal of Plasticity, 24(1), pp. 55-73. (doi:10.1016/j.ijplas.2007.01.013)

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Abstract

The initial boundary value problem corresponding to a model of strain gradient plasticity due to [Gurtin, M., Anand, L., 2005. A theory of strain gradient plasticity for isotropic, plastically irrotational materials. Part I: Small deformations. J. Mech. Phys. Solids 53, 1624–1649] is formulated as a variational inequality, and analysed. The formulation is a primal one, in that the unknown variables are the displacement, plastic strain, and the hardening parameter. The focus of the analysis is on those properties of the problem that would ensure existence of a unique solution. It is shown that this is the case when hardening takes place. A similar property does not hold for the case of softening. The model is therefore extended by adding to it terms involving the divergence of plastic strain. For this extended model the desired property of coercivity holds, albeit only on the boundary of the set of admissible functions.

Item Type:Articles
Keywords:elastic,gradient plasticity,microstructures a,plastic material b,variational calculus c
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:McBride, Dr Andrew
Authors: Reddy, B. D., Ebobisse, F., and McBride, A.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:International Journal of Plasticity
Publisher:Elsevier
ISSN:0749-6419
ISSN (Online):1879-2154

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