By Mauro Ferrari, Vladimir T. Granik, Ali Imam, Joseph C. Nadeau
The lately proposed, absolutely multi-scale conception of doublet mechanics, awarded the following in a self-contained shape, deals unprecented possibilities to reconcile the discrete and continuum representations of solids whereas retaining an easy analytical layout and whole compatibility with lattice dynamics and continuum mechanics. Its purposes comprise micro-electro-mechanical platforms (MEMS), granular and particulate media, nanotubes and peptide arrays. Novel effects are pronounced, together with the identity of a brand new type of dispersive floor waves, and the presentation of tools for the experimental choice of the fundamental microstructural parameters. The relationships among doublet mechanics, lattice dynamics, and continuum theories are tested.
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Additional info for Advances in Doublet Mechanics
Doublet Thermomechanics (K. Mon and M. 4 Superposed Rigid Body Motions In the various theories of solid mechanics, once a set of measures of the deformation are chosen, these measures are tested against transformations of the deformed configuration to check whether they are properly invariant. Thus, in finite deformation theories of classical continuum mechanics, the CauchyGreen tensor C = FTF is chosen as a strain measure and is determined to be invariant under arbitrary finite rigid motion of the deformed configuration.
M}; m = 2n; and n is the valence of the Bravais lattice. For spherical particles whose nodes a E the valence n ranges from 3 to 6. ) structures have the valence n = 3 and n = 6, respectively (see Figs. 3). The FCCS is also called pyramidal. For Bravais lattices the bundle Tm (a) admits a decomposition into two disjoint subsets T: (a) and T; (a) which are equivalent via the center of r. 4 Microstructure, Measures of Deformations, Field Equations A Fig. 1. Particle doublet (A, B cr ). A-A Fig. 2.
G. Day (1977), Green and Naghdi (1977), Naghdi (1980), Kestin (1990)) and much of it has centered around using the Clausius-Duhem Inequality (CDI) as the embodiment of the Second Law of Thermodynamics and its use to derive constitutive restrictions in the manner proposed by Coleman and Noll (1963). e. the CDI can be satisfied by any of a range of entropy values. Green and Naghdi (1977) have shown that the CDI predicts, for a class of rigid heat conductors in equilibrium, that if heat is added to the medium, temperature must decrease.
Advances in Doublet Mechanics by Mauro Ferrari, Vladimir T. Granik, Ali Imam, Joseph C. Nadeau