A diffuse interface model for microstructural evolution in elastically stressed solids

P. H. Leo, J. S. Lowengrub, H. J. Jou

Research output: Contribution to journalArticle

141 Citations (Scopus)

Abstract

We present a diffuse interface (DI) model for capturing microstructure formed during the coarsening of a two dimensional, elastically stressed binary alloy. The DI model is based on a generalized Cahn-Hilliard free energy; evolution occurs to lower the free energy. Using a matched asymptotic expansion, we show that the DI model converges to a well-studied sharp interface system as the thickness of the diffuse interface approaches zero. Numerical simulations confirm this equivalence. We develop pseudo-spectral numerical methods to solve the DI system and we carefully investigate the dependence of results on numerical parameters. The DI model is used to follow microstructural evolution through topological transitions such as particle merging and vanishing. We show that in isotropic media, elastic inhomogeneity may lead to interesting topology changes such as a reversal of the roles of the precipitate and matrix phases.

Original languageEnglish (US)
Pages (from-to)2113-2130
Number of pages18
JournalActa Materialia
Volume46
Issue number6
DOIs
StatePublished - Mar 23 1998

Fingerprint

Microstructural evolution
Free energy
Binary alloys
Coarsening
Merging
Interfaces (computer)
Precipitates
Numerical methods
Topology
Microstructure
Computer simulation

Cite this

A diffuse interface model for microstructural evolution in elastically stressed solids. / Leo, P. H.; Lowengrub, J. S.; Jou, H. J.

In: Acta Materialia, Vol. 46, No. 6, 23.03.1998, p. 2113-2130.

Research output: Contribution to journalArticle

Leo, P. H. ; Lowengrub, J. S. ; Jou, H. J. / A diffuse interface model for microstructural evolution in elastically stressed solids. In: Acta Materialia. 1998 ; Vol. 46, No. 6. pp. 2113-2130.
@article{1271c65a5ef54671869fd1d2189c14f3,
title = "A diffuse interface model for microstructural evolution in elastically stressed solids",
abstract = "We present a diffuse interface (DI) model for capturing microstructure formed during the coarsening of a two dimensional, elastically stressed binary alloy. The DI model is based on a generalized Cahn-Hilliard free energy; evolution occurs to lower the free energy. Using a matched asymptotic expansion, we show that the DI model converges to a well-studied sharp interface system as the thickness of the diffuse interface approaches zero. Numerical simulations confirm this equivalence. We develop pseudo-spectral numerical methods to solve the DI system and we carefully investigate the dependence of results on numerical parameters. The DI model is used to follow microstructural evolution through topological transitions such as particle merging and vanishing. We show that in isotropic media, elastic inhomogeneity may lead to interesting topology changes such as a reversal of the roles of the precipitate and matrix phases.",
author = "Leo, {P. H.} and Lowengrub, {J. S.} and Jou, {H. J.}",
year = "1998",
month = "3",
day = "23",
doi = "10.1016/S1359-6454(97)00377-7",
language = "English (US)",
volume = "46",
pages = "2113--2130",
journal = "Acta Materialia",
issn = "1359-6454",
publisher = "Elsevier Limited",
number = "6",

}

TY - JOUR

T1 - A diffuse interface model for microstructural evolution in elastically stressed solids

AU - Leo, P. H.

AU - Lowengrub, J. S.

AU - Jou, H. J.

PY - 1998/3/23

Y1 - 1998/3/23

N2 - We present a diffuse interface (DI) model for capturing microstructure formed during the coarsening of a two dimensional, elastically stressed binary alloy. The DI model is based on a generalized Cahn-Hilliard free energy; evolution occurs to lower the free energy. Using a matched asymptotic expansion, we show that the DI model converges to a well-studied sharp interface system as the thickness of the diffuse interface approaches zero. Numerical simulations confirm this equivalence. We develop pseudo-spectral numerical methods to solve the DI system and we carefully investigate the dependence of results on numerical parameters. The DI model is used to follow microstructural evolution through topological transitions such as particle merging and vanishing. We show that in isotropic media, elastic inhomogeneity may lead to interesting topology changes such as a reversal of the roles of the precipitate and matrix phases.

AB - We present a diffuse interface (DI) model for capturing microstructure formed during the coarsening of a two dimensional, elastically stressed binary alloy. The DI model is based on a generalized Cahn-Hilliard free energy; evolution occurs to lower the free energy. Using a matched asymptotic expansion, we show that the DI model converges to a well-studied sharp interface system as the thickness of the diffuse interface approaches zero. Numerical simulations confirm this equivalence. We develop pseudo-spectral numerical methods to solve the DI system and we carefully investigate the dependence of results on numerical parameters. The DI model is used to follow microstructural evolution through topological transitions such as particle merging and vanishing. We show that in isotropic media, elastic inhomogeneity may lead to interesting topology changes such as a reversal of the roles of the precipitate and matrix phases.

UR - http://www.scopus.com/inward/record.url?scp=0032010562&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032010562&partnerID=8YFLogxK

U2 - 10.1016/S1359-6454(97)00377-7

DO - 10.1016/S1359-6454(97)00377-7

M3 - Article

AN - SCOPUS:0032010562

VL - 46

SP - 2113

EP - 2130

JO - Acta Materialia

JF - Acta Materialia

SN - 1359-6454

IS - 6

ER -