By Mauro Ferrari, Vladimir T. Granik, Ali Imam, Joseph C. Nadeau
The lately proposed, absolutely multi-scale concept of doublet mechanics, awarded right here in a self-contained shape, deals unprecented possibilities to reconcile the discrete and continuum representations of solids whereas keeping an easy analytical layout and whole compatibility with lattice dynamics and continuum mechanics. Its purposes contain micro-electro-mechanical platforms (MEMS), granular and particulate media, nanotubes and peptide arrays. Novel effects are stated, together with the id of a brand new type of dispersive floor waves, and the presentation of equipment for the experimental decision of the fundamental microstructural parameters. The relationships among doublet mechanics, lattice dynamics, and continuum theories are tested.
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Additional resources for Advances in Doublet Mechanics
This approach readily leads to a restatement of eqn. 44) 48 3. Multi-Component Constitutive Equations (K. Mon and M. Ferrari) from a summation of eqn. 1). -Tak 1 ···Tak x X 0=1 X=1 8 X (Pai + tai) ~ 8x ... 45 ) a=1 where the partial derivative has replaced the material time derivative on the right hand side. 40) remain unchanged in form. Similar to the treatment presented in Chap. 43) leads to the conclusion that the DM microstrain measures are properly invariant. 51) where T/3 is the magnitude of ,/3.
10) represents the unit micro-elongation or elongation microstrain of an arbitrary doublet. , 1/::::"u o 1« "10 and fa « 1, respectively. 11) "10 then follows. Substituting /::::"u o from eqn. 5) into eqn. 11) and using eqns. , xk 1 ' ••• ,Xk". Each subscript of the set k1 , ••• ,kx runs through the integers 1,2,3. It should be noted that the elongation microstrain fa of the doublet (A, B o ) is caused by the motion of the node bo E B o away from node a E A along the vector To. Therefore, this microstrain can be conveniently represented as €o = fa To.
Elastic spheres of diameter d. The particles are either in contact with each other or separated by adhesive layers. To simplify the problem without losing its main features, we assume that the set H o (the subscript 0 indicates the initial state of H) is regular: the centers of the particles, or nodes, form a Bravais lattice A couple of adjacent particles A and B in H o represents a doublet (A, B) with the vector-axis Co emerging from the node a E A toward the node b E B (Fig. 1). The respective unit vector is TO Co /"7 where "7 =1 Co 1denotes the distance between a and b.