Calculus of Variations and Geometric Measure Theory

N. Ansini - F. Ebobisse

Homogenization of periodic multi-dimensional structures: The linearly elastic/perfectly plastic case

created on 16 Dec 2001


Published Paper

Inserted: 16 dec 2001

Journal: Adv. Math. Sci. Appl.
Volume: 11
Number: 1
Pages: 203-225
Year: 2001


In this paper we study the asymptotic behaviour via $\Gamma$-convergence of some integral functionals $F_{\epsilon}$ which model some multi-dimensional structures and depend explicitly on the linearized strain tensor. The functionals $F_{\epsilon}$ are defined in particular classes of functions with bounded deformation while the limit problem is set in the usual framework of Sobolev spaces or $BD(\Omega)$. We also construct an example of such functionals showing that under some special assumptions we can have non local effects.

Keywords: Homogenization, $\Gamma$-convergence, Korn's inequality, Functions with bounded deformation