By Y. L. Bai, H. Y. Wang, M. F. Xia, F. J. Ke (auth.), G. C. Sih (eds.)
This quantity on multiscaling has been encouraged by way of the development of nano-technology long ago 4 a long time. specifically, nano-electronics has cleared the path to teach that the habit of nano-size our bodies are usually not basically diverse from macro-size our bodies yet they don't obey an identical actual legislation. There seems to be a mesoscopic sector which separates the legislation of quantum physics and continuum mechanics. a spot has been left within the complete diversity of scaling from macro to nano. Micro-manipulation will be made better if the atomic and molecular scale actions should be pointed out extra accurately with the use particular goals. during this admire, fabric technological know-how has already benefited by means of positioning and structuring of nanometer-scale debris to reach on the wanted macroscopic fabric houses. the belief has been applied to tailor-make structural fabrics for the Boeing 787 to raised accommodate non-uniform pressure and pressure at varied destinations of the plane. Explored also are the opportunity of coaxing DNA-based organisms akin to viruses to enhance functionality of batteries, sun cells, materials, paints and different kinds of fabrics. the potential for assembling bio-molecules to construct digital elements can be within the making plans. The manipulation of molecules and atoms has been considered as a typical base for either fabric and lifestyles technological know-how. Quantum and continuum mechanics are being utilized part via aspect for exploring the habit of small and big gadgets relocating at speedy and sluggish speed.
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Additional info for Multiscaling in Molecular and Continuum Mechanics: Interaction of Time and Size from Macro to Nano: Application to biology, physics, material science, mechanics, structural and processing engineering
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P. Chen et al. and the total displacement of the α-th atom in k-th unit cell as u (k, α ) = u (k) + ȟ (k, α ) (8) The total atomic displacement of atom (k, α) is again expressed as a sum of a homogeneous lattice deformation u(k) and an inhomogeneous internal deformation ξ (k,α). 3 Breakdown of classical continuum mechanics Classic continuum mechanics views a crystal as a homogeneous and continuous medium rather than a periodic array of atomic bonding units. The basic structural unit of the crystal is taken without structure and is idealized as point mass.
4, and the comparison with non interactive single-scale homogenization and interactive multi-scale approach clearly demonstrates how the conventional non interactive single-scale homogenization approach is incapable of capturing the localized winkling response. S. Chen and S. Mehraeen Fig. 2. 15µm). Wrinkling formation in polycrystalline materials 19 Fig. 3. Comparison of vertical load-displacement curves of single-scale and multi-scale predictions, as well as experimental data [0]. Fig. 4. Comparison of large degree bending deformation predicted by non interactive single-scale homogenization and interactive multi-scale homogenization.
This implies ρα E α = n ¦[ k =1 1 2 m α (V kα ) 2 + U kα ]δ(R k − x)δ( ∆r kα − y α ) (48) The local density of internal energy, which is the state function of thermodynamics, can be expressed as the sum of thermal energy and potential energy ρα ε α = n ¦[ k =1 1 2 kα )2 + U kα ]δ(R k − x)δ(∆r kα − y α ) mα (V (49) Y.. P. Chen et al. 8 Heat flux The flow of energy by atomic motion, for all particles in the volume ǻV , gives the kinetic contributions to the energy flux. It comes from the rate at which the local energy E i of atom i moves with the local atomic velocity pi /mi , Q ikin = − pi i E mi (52) The potential contribution to the energy flow occurs whenever two moving particles interact in such a way that one particle transfers a part of their joint energy to the other particle.