On the thermodynamics of the Swift-Hohenberg theory

被引：7

作者：

Espath, L. F. R. ^{[1
]}

Sarmiento, A. F. ^{[1
]}

Dalcin, L. ^{[2
]}

Calo, V. M. ^{[3
,4
]}

机构：

[1] King Abdullah Univ Sci & Technol, Comp Elect & Math Sci & Engn, Thuwal 239556900, Saudi Arabia

[2] King Abdullah Univ Sci & Technol, Extreme Comp Res Ctr, Thuwal 239556900, Saudi Arabia

[3] Curtin Univ, Western Australian Sch Mines, Appl Geol, Fac Sci & Engn, Perth, WA 6845, Australia

[4] CSIRO, Mineral Resources, Kensington, WA 6152, Australia

来源：

CONTINUUM MECHANICS AND THERMODYNAMICS | 2017年 / 29卷 / 06期

关键词：

Phase-field; Gradient theory; Thermodynamics of continua; Swift-Hohenberg theory; CAHN-HILLIARD EQUATIONS; ORDER-PARAMETER; NAVIER-STOKES; FIELD; TRANSITIONS; BALANCES; FLOW;

D O I：

10.1007/s00161-017-0581-y

中图分类号：

O414.1 [热力学];

学科分类号：

摘要：

We present the microbalance including the microforces, the first- and second-order microstresses for the Swift-Hohenberg equation concomitantly with their constitutive equations, which are consistent with the free-energy imbalance. We provide an explicit form for the microstress structure for a free-energy functional endowed with second-order spatial derivatives. Additionally, we generalize the Swift-Hohenberg theory via a proper constitutive process. Finally, we present one highly resolved three-dimensional numerical simulation to demonstrate the particular form of the resulting microstresses and their interactions in the evolution of the Swift-Hohenberg equation.

引用

页码：1335 / 1345

页数：11

共 23 条

[1] THE THERMODYNAMICS OF ELASTIC MATERIALS WITH HEAT CONDUCTION AND VISCOSITY [J].

COLEMAN, BD ;

NOLL, W .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1963, 13 (03) :167-178

[2] PetIGA: A framework for high-performance isogeometric analysis [J].

Dalcin, L. ;

Collier, N. ;

Vignal, P. ;

Cortes, A. M. A. ;

Calo, V. M. .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2016, 308 :151-181

[3]

dell'Isola F, 2011, CISM COURSES LECT, V535, P17

[4] Energy exchange analysis in droplet dynamics via the Navier-Stokes-Cahn-Hilliard model [J].

Espath, L. F. R. ;

Sarmiento, A. F. ;

Vignal, P. ;

Varga, B. O. N. ;

Cortes, A. M. A. ;

Dalcin, L. ;

Calo, V. M. .

JOURNAL OF FLUID MECHANICS, 2016, 797 :389-430

[5] On the relationship between supplemental balances in two theories for pure interface motion [J].

Fried, E .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2006, 66 (04) :1130-1149

[6] CONTINUUM THEORY OF THERMALLY-INDUCED PHASE-TRANSITIONS BASED ON AN ORDER-PARAMETER [J].

FRIED, E ;

GURTIN, ME .

PHYSICA D-NONLINEAR PHENOMENA, 1993, 68 (3-4) :326-343

[7] DYNAMIC SOLID-SOLID TRANSITIONS WITH PHASE CHARACTERIZED BY AN ORDER-PARAMETER [J].

FRIED, E ;

GURTIN, ME .

PHYSICA D, 1994, 72 (04) :287-308

[8] Continua described by a microstructural field [J].

Fried, E .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1996, 47 (01) :168-175

[9] Tractions, balances, and boundary conditions for nonsimple materials with application to liquid flow at small-length scales [J].

Fried, Eliot ;

Gurtin, Morton E. .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2006, 182 (03) :513-554

[10]

Gurtin M.E., 2010, THE MECHANICS AND THERMODYNAMICS OF CONTINUA

← 1 2 3 →