By Mauro Ferrari, Vladimir T. Granik, Ali Imam, Joseph C. Nadeau

ISBN-10: 3540620613

ISBN-13: 9783540620617

The lately proposed, absolutely multi-scale thought of doublet mechanics, offered the following in a self-contained shape, deals unprecented possibilities to reconcile the discrete and continuum representations of solids whereas preserving 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 id of a brand new category of dispersive floor waves, and the presentation of equipment for the experimental selection of the fundamental microstructural parameters. The relationships among doublet mechanics, lattice dynamics, and continuum theories are tested.

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**Sample text**

36) = - Midrl. 8Xkr+l • • • 8Xkx Here n denotes the outward unit normal to the surface S. The subscript r = 1, ... , M - 1 if M ~ 2, and r = 1 if M = 1. However, r should be such that r + 1 < X otherwise one has to take the product T~k r+l ••• T~k x = 1 and to ignore the differential operator in eqns. ). To clarify the indicial convention, let M = 3. Then the maximum value of r is r = M - 1 = 2, and eqn. J 0 T ak l [( tai + Pai ) 0'=1 TJa a( tai + Pai) 2' Tak 2 a 0 - Xk 2 . + (TJa)2 3'• 2 0 0 Tak2 Taka 8 (tai 8 Xk 2 + pai)] 8 Xk a _"".

Additionally, the microstresses are required to satisfy the balance of linear momentum, n M X-I L L( -1)X-l~ X. , {)X( 0 Tak a=lx=1 ••• 1 0 Tak x {) t) Pai +{) Xk ••• 1 ai Xk x + p. 'I, - ... 7) and moment of momentum, n L (€ijqT~lQq a=1 where Pi is the volume body force, Li is the volume distribution of body couples, and Eijk is the permutation tensor. The summing limit, M, refers to the degree of approximation. The independent variables in the above treatment are {u, cjJ, T}. 10) 30 2. Doublet Thermomechanics (K.

68) 5. 72) where 1(3 is the magnitude of 'Y(3. 6. 76) M3 abCb, b=l with the conditions A o(3 = A(3o, E o(3 = E(3o, I o(3ij = I(3oji, B o(3 = D(3o, and M3 ab = M3ba.

### Advances in Doublet Mechanics by Mauro Ferrari, Vladimir T. Granik, Ali Imam, Joseph C. Nadeau

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