[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Mechanical properties of nanocrystalline materials

Fractional Differential Equations

Dislocation theory is used to invoke a strain gradient theory of rate independent plasticity. Hardening is assumed to result from the accumulation of both randomly stored and geometrically necessary dislocation. The density of the geometrically necessary dislocations scales with the gradient of plastic strain. A deformation theory of plasticity is introduced to represent in a phenomenological manner the relative roles of strain hardening and strain gradient hardening. The theory is a non-linear generalization of Cosserat couple stress theory. Tension and torsion experiments on thin copper wires confirm the presence of strain gradient hardening. The experiments are interpreted in the light of the new theory.

Strain gradient plasticity: Theory and experiment

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

On the Microstructural Origin of Certain Inelastic Models

On the role of gradients in the localization of deformation and fracture

The physics of plastic deformation

http://users.auth.gr/~akonsta/2011_Gradient%20elasticity%20in%20statics%20and%20dynamics.pdf

Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results

It is shown that the phenomenon of strength dependence on size, for otherwise geometrically similar specimens, may be interpreted on the basis of gradient elasticity and gradient plasticity arguments. This is illustrated by adopting a simple strength of materials approach for considering torsion and bending of solid bars and subsequent comparison with available experimental data. Solutions of boundary value problems based on gradient elasticity and gradient plasticity including those of fracture and shear banding can also be used to interpret size effects in more complex situations. This is not discussed here, however, in order to maintain simplicity and clarity when illustrating the theoretical predictions in comparison with the experimental trends.

Elias C. Aifantis

Papers

On the Microstructural Origin of Certain Inelastic Models

On the role of gradients in the localization of deformation and fracture

The physics of plastic deformation

Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results

Strain gradient interpretation of size effects