We consider a variational model which describes a complex system composed, in its reference configuration, of a periodic distribution of "small" interacting particles immersed in a continuous medium. We describe its macroscopic limit via Gamma-convergence, highlighting different regimes. In particular, we show how the interplay between the particles and the continuum leads, for a critical size of the particles, to a capacitary term. Eventually, we discuss how the presence of a continuum affects the properties of the ground states of the system of particles in terms of the validity or not of the so-called "Cauchy-Born" rule.

A variational model of interaction between continuum and discrete systems / Roberto, Alicandro; Ansini, Nadia. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - ELETTRONICO. - 24:10(2014), pp. 1957-2008. [10.1142/s0218202514500134]

A variational model of interaction between continuum and discrete systems

ANSINI, NADIA
2014

Abstract

We consider a variational model which describes a complex system composed, in its reference configuration, of a periodic distribution of "small" interacting particles immersed in a continuous medium. We describe its macroscopic limit via Gamma-convergence, highlighting different regimes. In particular, we show how the interplay between the particles and the continuum leads, for a critical size of the particles, to a capacitary term. Eventually, we discuss how the presence of a continuum affects the properties of the ground states of the system of particles in terms of the validity or not of the so-called "Cauchy-Born" rule.
2014
perforated domains; Gamma-convergence; atomistic-to-continuum limit
01 Pubblicazione su rivista::01a Articolo in rivista
A variational model of interaction between continuum and discrete systems / Roberto, Alicandro; Ansini, Nadia. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - ELETTRONICO. - 24:10(2014), pp. 1957-2008. [10.1142/s0218202514500134]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/556710
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