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The design of metamaterials using generalised continua as mathematical models: numerics, experiments and theory

le 19 janvier 2017

Francesco dell'Isola, professeur à l'Université de Rome 'La Sapienza' et membre du M&MoCS (International Research Center for Mathematics & Mechanics of Complex Systems), interviendra lors du séminaire.

Mathematics sometimes seems to be regaining its role in applied mechanics. The present attitude of applied scientists towards mathematics and abstraction is indeed rather hostile. It seems that one can distinguish some cyclicality in this attitude and in its change towards the opposite one, which we could call Archimedean attitude. This last considers mathematics as ancilla et regina scientiarum or in other words the most fundamental tool which we have to explore and control phenomena. The cycle which we are living can be called, following the epistemological vision by Giambattista Vico, as a ricorso : i.e. a regressive stage of the societies experienced after a progressive stage, which he calls a  corso.  The historical corso when mathematics supplied sciences with the powerful thrust which lead (finally) to modern technology started actually with the Age of Enlightenment (le Siècle des Lumières) and found D'Alembert and Lagrange as his main characters (at least in Mechanical sciences). 

The contingent circumstance for the return to mathematics concerns one of the last challenges in engineering sciences: we mean the effort to design metamaterials (or architectured materials). Actually such a challenge can be formulated as follows: to find a way for building a material whose behaviour is specified a priori via some specific demands. We are talking about: materials on demand. How can we characterise the peculiar behaviour of a specifically demanded material? Simply by specifying the equations that must govern the behaviour of such a material. In other words: if the synthesis of metamaterials consists in finding the way to construct fabrics whose global behaviour is tailored for a specific application or requirement, we specify such requirement or behaviour by means of the governing equations which we impose to be valid to describe the desired material. Therefore the old problem of synthesis of electronic circuits for obtaining analogic computers finds a renewed life in a slightly different context. It can be reformulated as follows: Given the governing equations one has to find the microstructure that describe them macroscopically. The parallel development of 3D printing technologies made this endeavour realizable also in practice. Some theoretical, experimental and numerical results will be presented: they show how the "ancient" theory of generalized continua finds new, beautiful and promising applications. In particular the exotic behaviour of pantographic structures is described and analyses.

Type :
Séminaires - conférences
Lieu(x) :
Campus de Cachan
Amphi e-média
Bâtiment Léonard De Vinci - ENS Cachan
61, avenue du Président Wilson 94230 Cachan
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