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Journal of the Mechanics and Physics of Solids 57 (2009) 1749–1779
Contents lists available at ScienceDirect
Journal of the Mechanics and Physics of Solids
journal homepage: ate/jmps
Gradient nanoscale polycrystalline elasticity: Intergrain interactions
and triple-junction conditions
Eliot Fried a,Ã, Morton E. Gurtin b
a Department of Mechanical Engineering, McGill University, Montre´al, Que´bec, Canada H3A 2K6
b Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA
article info abstract
Article history: Using the principle of virtual power, we develop general balance equations, interface
Received 20 October 2008 conditions, triple-junction conditions, and boundary conditions for second-grade
Received in revised form nanocrystalline elastic materials undergoing infinitesimal deformations. We further
25 March 2009 develop thermodynamically consistent constitutive equations and provide a weak
Accepted 18 June 2009
formulation of resulting boundary-value problems that automatically yields internal
conditions such those that hold across interfaces and at triple junctions.
Keywords: & 2009 Elsevier Ltd. All rights reserved.
Nanoscale polycrystalline elasticity
Grain boundaries
Grain junctions
Hypertraction
Hyperstress
1. Introduction
Because the theory we develop is plicated, we begin with an outline stressing the central ideas and
results, but omitting all analysis.
. Background
A nanocrystalline material is a polycrystal with a grain size of characteristic linear dimension less than 100 nm.
Consistent with the observation that the stress needed to generate a dislocation in a crystal grain of characteristic linear
dimension d scales with dÀ1 ln d,1 experiments2 and atomistic simulations3 show that intragranular inelasticity is largely
negligible in nanocrystalline materials. Intergranular inelasticity associated with the generation of dislocations at grain
boundaries