On certain problems of deformation-induced material instabilities
Document Type
Article
Publication Date
10-2012
Department
Department of Mechanical Engineering-Engineering Mechanics
Abstract
Deformation-induced material instabilities may be of elastic (buckling, martensitic transformations) or plastic (necking/shear banding, dislocation patterning) type. In plasticity, the emergence of material instabilities is mainly associated with the properties of the underlying microstructure such as the motion, interaction and production/annihilation of dislocations: the carriers of plastic deformation. In any case, a common mathematical basis for describing the emergence and evolution of pattern-forming material instabilities in a large class of physical problems may be sought on non-monotonous equations of state, in conjunction with the introduction of suitable time and space derivatives in the state variables. This was an approach elaborated upon by Aifantis and co-workers in the early eighties for plastic instabilities. In about the same time, a similar and perhaps broader approach, based on a non-convex energy functional for various physical systems and the introduction of higher-order field variables to stabilize the behavior in the non-convex regime, was independently proposed by Berdichevsky and co-workers. This paper, written on the occasion of his 65th birthday, provides an updated discussion of dislocation patterning, shear banding and strain instabilities during epitaxial film growth.
Publication Title
International Journal of Engineering Science
Recommended Citation
Walgraef, D.,
&
Alfantis, E.
(2012).
On certain problems of deformation-induced material instabilities.
International Journal of Engineering Science,
59, 140-155.
http://doi.org/10.1016/j.ijengsci.2012.03.017
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/6519
