Publication detail

Homogenization of discrete diffusion models by asymptotic expansion

ELIÁŠ, J. YIN, H. CUSATIS, G.

Original Title

Homogenization of discrete diffusion models by asymptotic expansion

Type

journal article in Web of Science

Language

English

Original Abstract

Diffusion behaviors of heterogeneous materials are of paramount importance in many engineering problems. Numerical models that take into account the internal structure of such materials are robust but computationally very expensive. This burden can be partially decreased by using discrete models, however even then the practical application is limited to relatively small material volumes. This paper formulates a homogenization scheme for discrete diffusion models. Asymptotic expansion homogenization is applied to distinguish between (i) the continuous macroscale description approximated by the standard finite element method and (ii) the fully resolved discrete mesoscale description in a local representative volume element (RVE) of material. Both transient and steady-state variants with nonlinear constitutive relations are discussed. In all the cases, the resulting discrete RVE problem becomes a simple linear steady-state problem that can be easily pre-computed. The scale separation provides a significant reduction of computational time allowing the solution of practical problems with a~negligible error introduced mainly by the finite element discretization at the macroscale.

Keywords

homogenization; mass transport; diffusion; discrete model; concrete; Poisson's equation; quasi-brittle material

Authors

ELIÁŠ, J.; YIN, H.; CUSATIS, G.

Released

1. 11. 2022

Publisher

Wiley

ISBN

0363-9061

Periodical

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS

Year of study

46

Number

16

State

United Kingdom of Great Britain and Northern Ireland

Pages from

3052

Pages to

3073

Pages count

21

URL

https://onlinelibrary.wiley.com/doi/full/10.1002/nag.3441

BibTex

@article{BUT178706,
  author="Jan {Eliáš} and Hao {Yin} and Gianluca {Cusatis}",
  title="Homogenization of discrete diffusion models by asymptotic expansion",
  journal="INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS",
  year="2022",
  volume="46",
  number="16",
  pages="3052--3073",
  doi="10.1002/nag.3441",
  issn="0363-9061",
  url="https://onlinelibrary.wiley.com/doi/full/10.1002/nag.3441"
}