Homogenization of discrete thin structures

被引：4

作者：

Braides, Andrea ^{[1
]}

D'Elia, Lorenza ^{[2
]}

机构：

[1] SISSA, Via Bonomea 265, Trieste, Italy

[2] TU Wien, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, Vienna, Austria

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2023年 / 231卷

基金：

奥地利科学基金会;

关键词：

Thin structures; Dimension reduction; Discrete-to-continuum; Lattice systems; Homogenization; CONTINUUM LIMITS; FILMS; ENERGIES; MODEL;

D O I：

10.1016/j.na.2022.112951

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider graphs parameterized on a portion X & SUB; Zd x {1,. .. , M}k of a cylindrical subset of the lattice Zd x Zk, and perform a discrete-to-continuum dimension-reduction process for energies defined on X of quadratic type. Our only assumptions are that X be connected as a graph and periodic in the first d-directions. We show that, upon scaling of the domain and of the energies by a small parameter & epsilon;, the scaled energies converge to a d-dimensional limit energy. The main technical points are a dimension-reducing coarse-graining process and a discrete version of the p-connectedness approach by Zhikov.& COPY; 2022 Elsevier Ltd. All rights reserved.

引用

页数：27

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