Advances in Doublet Mechanics, Volume 45
The recently proposed, fully multi-scale theory of doublet mechanics offers unprecented opportunities to reconcile the discrete and continuum representations of solids while maintaining a simple analytical format and full compatibility with lattice dynamics and continuum mechanics. In this monograph, a self-contained account of the state of the art in doublet mechanics is presented. Novel results in the elastodynamics of microstructured media are reported, including the identification of a new class of dispersive surface waves, and the presentation of methods for the experimental determination of the essential microstructural parameters. The relationships between doublet mechanics, lattice dynamics, and continuum theories are examined, leading to the identification of the subject areas in which the use of doublet mechanics is most advantageous. These areas include the analysis of domains as diverse as micro-electro-mechanical systems (MEMS), granular and particulate media, nanotubes, and peptide arrays.
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amplitude ratios application approximation of DM arbitrary assumed balance laws boundary conditions boundary problems Bravais lattice carbon nanotubes Chap classical elasticity components consider constants constitutive equations continuum mechanics cos2 Cosserat crystal deformation differential dimensionless scale factor displacement field doublet mechanics doublet microstresses elongation entropy equations of motion Ferrari finite Flamant problem follows function given in eqn governing equations Granik and Ferrari granular media Green and Naghdi homogeneous incident angle incident P-wave infinite interatomic isotropic kinematic lattice dynamics linear elastic macroscopic materials of grade micro microconstants microforces micromechanical microstrains microstructure mode conversion angle multi-scale multi-wall node nonlocal nonscale obtained Phase changes phase velocity Poisson's ratio propagation real solid reflected P-wave rotations scale parameter Sect shear simple cubic solids with microstructure solution stress structure surface wave tensor theories of elasticity tion torsion traction tube vector view of eqns wavelength yields zero