Continuum approaches applied to discrete periodic media

Objectives : This research project focuses on the behavior of discrete elastic media (or lattice elastic media), using the mechanics of nonlocal or generalized continuous media. It has already been shown that one-dimensional lattices such as discrete strings, bars or beams can be equivalently modelled by one-dimensional non-local or enriched models. The two or three-dimensional generalization of such lattice-based nonlocal or enriched continua modelling is much more recent, and has mainly focused on the behavior of microstructured plates or even three-dimensional simple lattices. The non-local or gradient-type laws that emerge from a continualization procedure of such 2D or 3D lattices may be used for the analysis of the stability and the vibration of these so-called microstructured systems. Surprising results may emerge for these discrete systems, that cannot be captured by simple continuous media.

Expectations : This research has applications in all areas of engineering sciences (including applied physics, mechanical or civil engineering) concerned with the paradigm of changes of scale. For nanotechnology applications, the study of nanoscale structures requires the introduction of consistent structural models, that include interatomic scale effects. More generally, a multi-scale structural analysis driven by the behavior of constituent materials at both the micro and the macro scale requires the formulation of specific laws, that make the material and the structure interact through a non-local correspondence.

Key words

Lattice; Beam theory; Plate theory; Nonlocal elasticity; Asymptotic methods; Scale effects; Shear effects; Microstructured theories

Funding category: Contrat doctoral

Financement de l'Université de l'Aquila (Italie)

PHD Country: France