Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
799766 | Journal of the Mechanics and Physics of Solids | 2010 | 12 Pages |
Abstract
Using an averaging procedure for large ensembles of dislocations, a basic but mathematically non-trivial modelling framework is developed for the transport of dislocation densities in a macroscopically homogeneous and isotropic film of a crystalline solid subjected to uniform shear. It has the form of a system of nonlinear, non-local partial differential equations of the first order with a source-type right-hand side. The solution to this system is studied numerically, and the associated average stress is evaluated as a function of time. The resulting stress-strain relations exhibit a size effect similar to those that previously motivated strain-gradient plasticity theories.
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Authors
K.D. Cherednichenko,