Scaling of Structural Strength
This book focuses on the effect of structure size on structural strength and failure behavior. The author shares his theories on size effects, and the result of quasibrittle materials.
TABLE OF CONTENTS Scaling of Structural Strength
Chapter 10: Size Effect at Continuum Limit on Approach to Atomic Lattice Scale
The recent emphasis of continuum mechanics studies on the transition from continuum to atomic lattice models implies interesting questions of scaling. Although the subject is not pertinent to quasibrittle and heterogeneous materials, the main focus of this book, a brief discussion (based on Ba ant 2001b) will be presented in this section because of methodological similarities in scaling, because of similarity of the objective (which is the strength or load capacity of structures), and because of the importance of the subject in nano-technology.
10.1. Scaling of Dislocation Based Strain-Gradient Plasticity
Building on the initial ideas of Toupin (1962) and Mindlin (1965), an impressive series of progressively refined studies extended to microscale the theory of metal plasticity (Fleck and Hutchinson 1993, 1997, Hutchinson 1997; Gao and Huang 2000). Careful physical arguments based on the theory of dislocations led Gao et al. (1999a,b) and Huang et al. (2000) to derive the following constitutive relation:
| (10.1) |  |
| (10.2) |  |
where
| (10.3) |  |
Figure 10.1: Illustration of the difference between (b) statistically stored dislocations and (e) geometrically necessary dislocations; (a,d) show the initial states of square lattices with 56 and 63 atoms, respectively, and (c) shows that for a homogeneous deformation no dislocations are necessary
and
| (10.4) |  |
Here K = elastic bulk modulus; 
= deviatoric strains, ? ik = 
( u i,k + u k,i) = strains; ?, ? = 2nd and 3rd order tensors of components ? ij, ? ijk; ? ijk = u k,ij =...
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