Lattice dynamics from a continuum viewpoint

M. Charlotte (1) , Lev Truskinovsky (2)

1 ICA - Institut Clément Ader
2 LMS - Laboratoire de mécanique des solides

We develop a novel continuum description of lattice dynamics for a particle chain with nearest neighbor interactions. Our continuum model interpolates discrete solutions and allows one to deal adequately with singular and impact loadings. The resulting theory is local in space and nonlocal in time. It is characterized by a nontrivial hereditary structure which blends inertial and elastic forces. The proposed methodology can be used to build continuum approximations for lattice dynamics which incorporate successively finer scales. It can also serve as a seamless interface between discrete and continuum elasticity theories.

Mots clés: Meta-materials; Lattice dynamics; Quasi-continuum modeling; Nonlocal elasticity; Discrete to continuum; Multiscale modeling; Non-Newtonian inertia

Domaines: Mécanique des matériaux [physics.class-ph]

M. Charlotte, Lev Truskinovsky. Lattice dynamics from a continuum viewpoint. Journal of the Mechanics and Physics of Solids, 2012, 60 (8), pp.1508-1544. ⟨10.1016/j.jmps.2012.03.004⟩. ⟨hal-01853071⟩