Relationship between the Macroscopic and Microscopic Theory of Crystal Elasticity. I. Primitive Crystals

Abstract

The general relationship between the macroscopic theory of crystal elasticity and a recently introduced microscopic formalism is established for primitive crystals. The relationship is more simple and direct than the corresponding relationship between the macroscopic theory and the Born-Huang formalism, which has to be established via sound-wave propagation. Additional conditions are derived for the Born-Huang formalism which remove an inconsistency in the microscopic theory and confirm that purely nearest-neighbor interactions must be central. The new macroscopic-microscopic relationship is applied to an illustrative study of the simple cubic structure which also shows that three of the six third-order elastic constants of the alkali halides depend on long-range interactions.

Non-hexagonal-ring defects and structures induced by healing and strain in graphene and functionalized graphene

“…In the figure, we show a map of the elastic energy of the supercell at three different stages of the plastic relaxation process, computed using a Keating model. 28 Figure 2(a) shows the elastic energy for the initial strained geometry. Note that, in this configuration, the strain energy is distributed nearly uniformly over the whole system, with a larger magnitude at the SW defect.…”

Percolation on Elastic Networks: New Exponent and Threshold

“…In both models (6) and (7), we assign a set of random numbers n ij9 between 0 to 1, on each bond of the lattice in each realization. Then we remove the bonds for which n u >p where p is decreased successively from unity.…”

Hybrid Lattice Particle Modelling Approach for Polymeric Materials Subject to High Strain Rate Loads

“…(1) Genuine 3D interaction force formulas that will be developed following Keating's approach [31]. (2) More adequate impact mode will be developed so as to accurately describe the shear friction between the projectile and the penetrated target.…”

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