A variational model of interaction between continuum and discrete systems

作者：Alicandro Roberto^*; Ansini Nadia

来源：Mathematical Models and Methods in Applied Sciences, 2014, 24(10): 1957-2008.

DOI：10.1142/S0218202514500134

• Atomistic-to-continuum limit
• perforated domains
• Gamma-convergence

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.

• 出版日期2014-9