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"From the bottom up": The basic mechanism of plastic deformation is the generation and motion of dislocations.
"From the bottom up": The basic mechanism of plastic deformation is the generation and motion of dislocations. Stochastic treatment of the dynamics of many interacting discrete dislocations generates a statistical hierarchy which provides, in principle, equations from which constitutive relations (interpreted as relations between ensemble-averaged quantities) can be derived. In practice, the hierarchy has to be closed at some level. The simplest closure, the mean-field approximation, yields the equations of classical continuum plasticity. Closure at the next level, allowing for pair correlations, generates non-local relations from which a strain-gradient correction to classical plasticity follows when the mean fields vary slowly relative to the scale of the dislocation microstructure. An explicit model for strain-gradient plasticity is thereby developed, in which the precise physical origin of the gradient terms is identified. Recent progress in this direction will be reported.
"From the top down": The limitation of the "bottom-up" approach is that it can only be carried through in idealised simple cases. It nevertheless assists in understanding what should underly any phenomenological gradient theory, and in identifying possible limitations. One feature of gradient theory of current interest is the identification of physically-realistic boundary conditions, and relations across interfaces, for the higher-order terms. These have a significant influence on the scale effects associated, for example, with grain size in a polycrystal. Illustrative results will be presented.
- Speaker
- Professor John R Willis FRS, University of Cambridge
- Venue
- Meston Lecture Theatre 1