Application of the element-free Galerkin method to nucleation of solid-solid phase transformations

Yi An Chu; Brian Moran

Application of the element-free Galerkin method to nucleation of solid-solid phase transformations

Yi An Chu^*, Brian Moran

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

1 Scopus citations

Abstract

A computational methodology for nucleation of phase transformations in a class of grade 2, nonlinearly elastic materials is presented. Nucleation is treated as an energy extremum problem. The material is assumed to be governed by a nonlinear, nonlocal elastic constitutive relation represented by a Landau-Ginzburg potential. The extremum problem is solved using the Element-Free Galerkin (EFG) method and a perturbed Lagrangian technique. The EFG method is used because of its ability to handle continuity of displacement gradients required in the weak form. Applications to nucleation in two-dimensions are presented which illustrate the accuracy of the method and its suitability for problem of this type.

Original language	English (US)
Pages (from-to)	135-147
Number of pages	13
Journal	American Society of Mechanical Engineers, Applied Mechanics Division, AMD
Volume	189
State	Published - 1994
Externally published	Yes
Event	Proceedings of the 1994 International Mechanical Engineering Congress and Exposition - Chicago, IL, USA Duration: Nov 6 1994 → Nov 11 1994

ASJC Scopus subject areas

Mechanical Engineering

Cite this

@article{9b37c93c9dca4e61adc65b9872b3026b,

title = "Application of the element-free Galerkin method to nucleation of solid-solid phase transformations",

abstract = "A computational methodology for nucleation of phase transformations in a class of grade 2, nonlinearly elastic materials is presented. Nucleation is treated as an energy extremum problem. The material is assumed to be governed by a nonlinear, nonlocal elastic constitutive relation represented by a Landau-Ginzburg potential. The extremum problem is solved using the Element-Free Galerkin (EFG) method and a perturbed Lagrangian technique. The EFG method is used because of its ability to handle continuity of displacement gradients required in the weak form. Applications to nucleation in two-dimensions are presented which illustrate the accuracy of the method and its suitability for problem of this type.",

author = "Chu, {Yi An} and Brian Moran",

year = "1994",

language = "English (US)",

volume = "189",

pages = "135--147",

journal = "American Society of Mechanical Engineers, Applied Mechanics Division, AMD",

issn = "0160-8835",

publisher = "American Society of Mechanical Engineers (ASME)",

note = "Proceedings of the 1994 International Mechanical Engineering Congress and Exposition ; Conference date: 06-11-1994 Through 11-11-1994",

}

TY - JOUR

T1 - Application of the element-free Galerkin method to nucleation of solid-solid phase transformations

AU - Chu, Yi An

AU - Moran, Brian

PY - 1994

Y1 - 1994

N2 - A computational methodology for nucleation of phase transformations in a class of grade 2, nonlinearly elastic materials is presented. Nucleation is treated as an energy extremum problem. The material is assumed to be governed by a nonlinear, nonlocal elastic constitutive relation represented by a Landau-Ginzburg potential. The extremum problem is solved using the Element-Free Galerkin (EFG) method and a perturbed Lagrangian technique. The EFG method is used because of its ability to handle continuity of displacement gradients required in the weak form. Applications to nucleation in two-dimensions are presented which illustrate the accuracy of the method and its suitability for problem of this type.

AB - A computational methodology for nucleation of phase transformations in a class of grade 2, nonlinearly elastic materials is presented. Nucleation is treated as an energy extremum problem. The material is assumed to be governed by a nonlinear, nonlocal elastic constitutive relation represented by a Landau-Ginzburg potential. The extremum problem is solved using the Element-Free Galerkin (EFG) method and a perturbed Lagrangian technique. The EFG method is used because of its ability to handle continuity of displacement gradients required in the weak form. Applications to nucleation in two-dimensions are presented which illustrate the accuracy of the method and its suitability for problem of this type.

UR - http://www.scopus.com/inward/record.url?scp=0028734525&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0028734525

SN - 0160-8835

VL - 189

SP - 135

EP - 147

JO - American Society of Mechanical Engineers, Applied Mechanics Division, AMD

JF - American Society of Mechanical Engineers, Applied Mechanics Division, AMD

T2 - Proceedings of the 1994 International Mechanical Engineering Congress and Exposition

Y2 - 6 November 1994 through 11 November 1994

ER -

Application of the element-free Galerkin method to nucleation of solid-solid phase transformations

Abstract

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this