ELFT HÍRADÓ

[Károlyi György <karolyi AT reak.bme.hu>]

Meghívó

Noël Challamel (Université de Bretagne Sud, Lorient,France):
Quasicontinuum: an intermediate state between discrete and continuous media
c. előadására

Időpont: 2016. május 18. szerda 10:30
Helyszín: Budapesti Műszaki és Gazdaságtudományi Egyetem
          Műegyetem rkp. 3.
          K épület 3. emelet 354/a terem.

Az előadás tartalma:

In this seminar, we will question the possibility to investigate discrete 
media such as lattices using quasicontinuum mechanics. Discrete media 
considered in this study are typically periodically microstructured media 
such as atomistic media, lattices, granular material or even truss structures 
for large scale applications. Quasicontinua may be defined as continuous 
media which behave like discrete media, but with a continuous formulation. 
Mathematically, the question is equivalent to approximate difference 
equations within some equivalent differential or partial differential 
equations, including possibly higher-order terms. From an engineering point 
of view, it is generally much simpler to investigate the behaviour of these 
discrete or microstructured media using continuum tools. The seminar will be 
mainly oriented towards the characterization of quasicontinua for structural 
mechanics applications.

Quasicontinua investigated in this study are of nonlocal or gradient types. 
It is shown that discrete strings (or lattice string) as already considered 
by Lagrange during the XVIIIth century may be revisited in the light of 
modern mechanics theories such as nonlocal mechanics. During the 19th 
century, Piola built some nonlocal-type or gradient-type media from discrete 
microscale interactions. Hencky-bar system, developed at the beginning of the 
XXth century can be considered as the paradigmatic bending lattice with 
inherent length scale. The nonlocal or gradient-type laws which emerge from a 
continualization procedure of such structural lattice are used for analysing 
some in-plane and out-of-plane beam instabilities problems and are then 
generalized to two-dimensional plate media. Geometrical and material 
non-linearities may be also accounted for at the lattice scale, thus 
generating some nonlocal or higher-order gradient laws at the macroscopic 
scale. 

Nonlocal structural mechanics is definitely an efficient engineering theory 
that may be able to capture the fundamental scale effects related to the 
microstructure at the finer scale. A lot of applications may be found in the 
small-scale world (especially for micromechanics or nanomechanics 
applications since the beginning of the XXIth century) but also for large 
scale civil engineering structures such as truss structures for instance. 
Discrete mechanics is not only a way to take into account rigorously the 
microstructure phenomena: it contributes to a better understanding of the 
fundamental behaviour of matter, following Bergson thoughts on the capability 
of our mind to better represent the reality by discontinuous objects.

"L’intelligence ne se représente clairement que le discontinu."
Henri Bergson


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