By Mauro Ferrari, Vladimir T. Granik, Ali Imam, Joseph C. Nadeau
The lately proposed, totally multi-scale thought of doublet mechanics, offered right here in a self-contained shape, bargains unprecented possibilities to reconcile the discrete and continuum representations of solids whereas preserving an easy analytical layout and entire compatibility with lattice dynamics and continuum mechanics. Its functions contain micro-electro-mechanical platforms (MEMS), granular and particulate media, nanotubes and peptide arrays. Novel effects are suggested, together with the id of a brand new type of dispersive floor waves, and the presentation of tools for the experimental choice of the basic microstructural parameters. The relationships among doublet mechanics, lattice dynamics, and continuum theories are tested.
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Extra resources for Advances in Doublet Mechanics
Treating chemical changes as a heat term is common in texts on nonequilibrium thermodynamics (DeGroot and Mazur 1962, Kirkaldy and Young 1987) and has the advantage that heat is easily measured since the energy change can be determined from the initial and terminal states of the system and the mechanical work can be determined independently from consideration of the laws of mechanics. The major disadvantage of treating chemical changes as a heat term stems from the loss of the usual association between heat and entropy.
Ferrari, V. T. Granik and A. 41 ) The superscript M gives the level of the approximation at which the macrostresses are represented by the microstresses. A brief digression is now undertaken in order to discuss the symmetry of the macroscopic stress tensor accounting for its scale dependence. Toward this objective a simplified system of equations is derived for the special case corresponding to the assumptions that Poi = 0, moi = 0 (doublet-level nonpolar medium) and toi depend only on X3. Furthermore, a simplified underlying microstructural geometry is assumed whereby T~i = 1 if a = i, T~i = 0 otherwise, and "10 = "1 > 0 for a = 1,2,3.
Generally, such treatments make use of different temperatures for each component. Controversies arise over which entropy inequality the components are required to satisfy and whether entropy inequalities that apply to the mixture as a whole can be validly applied to each component individually. Perhaps the most notable generalized continuum mechanical theory of mixtures is that due to Goodman and Cowin (1972) with later improvements by Passman (1977) and extension to reacting mixtures by Nunziato and Walsh (1980).