Macroscopic Description of Microscopically Strongly Inhomogenous Systems: A Mathematical Basis for the Synthesis of Higher Gradients Metamaterials

A Carcaterra (1, 2, 3) , F Dell 'Isola (1, 4) , R Esposito (1) , M Pulvirenti (1, 2)

1 M&MoCS - International Research Centre on Mathematics & Mechanics of Complex Systems
2 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]
3 CNIS-Centro per le Nanotecnologie Applicate all’Ingegneria, Roma
4 DIMA - Dipartimento di Ingegneria Meccanica e Aerospaziale [Roma La Sapienza]

We consider the time evolution of a one dimensional n-gradient continuum. Our aim is to construct and analyze discrete approximations in terms of physically realizable mechanical systems, called microscopic because they are living on a smaller space scale. We validate our construction by proving a convergence theorem of the microscopic system to the given continuum, as the scale parameter goes to zero.

Domaines: Physique mathématique [math-ph]

A Carcaterra, F Dell 'Isola, R Esposito, M Pulvirenti. Macroscopic Description of Microscopically Strongly Inhomogenous Systems: A Mathematical Basis for the Synthesis of Higher Gradients Metamaterials. Archive for Rational Mechanics and Analysis, 2015, 20 p. ⟨hal-01155474⟩