Chapter 10 - Size Effect at Continuum Limit on Approach to Atomic Lattice Scale

Abstract

Continuum mechanics studies imply interesting questions of scaling because of its importance in nanotechnology. The chapter illustrates difference between statistically stored dislocations and geometrically necessary dislocations, presents initial states of square lattices with 56 and 63 atoms, respectively, and explains that no dislocations are necessary for a homogeneous deformation. The small-size asymptotic behavior is closely approached only at sizes much smaller than the range of applicability of the strain-gradient theories of plasticity. The knowledge of this behavior is useful for developing asymptotic matching approximations for the realistic middle range. Knowledge of both large-size and small-size asymptotic behavior makes it possible to obtain good analytical approximations for the middle range of interest, agreeing with experimental as well as numerical results. The detrimental consequence of unrealistic small-size asymptotic properties is that the possibility of asymptotic matching approximations is lost.