A novel grain cluster-based homogenization scheme

D. D. Tjahjanto, P. Eisenlohr, F. Roters

Research output: Contribution to journalArticle

  • 13 Citations

Abstract

An efficient homogenization scheme, termed the relaxed grain cluster (RGC), for elasto-plastic deformations of polycrystals is presented. The scheme is based on a generalization of the grain cluster concept. A volume element consisting of eight (= 2 × 2 × 2) hexahedral grains is considered. The kinematics of the RGC scheme is formulated within a finite deformation framework, where the relaxation of the local deformation gradient of each individual grain is connected to the overall deformation gradient by the, so-called, interface relaxation vectors. The set of relaxation vectors is determined by the minimization of the constitutive energy (or work) density of the overall cluster. An additional energy density associated with the mismatch at the grain boundaries due to relaxations is incorporated as a penalty term into the energy minimization formulation. Effectively, this penalty term represents the kinematical condition of deformation compatibility at the grain boundaries. Simulations have been performed for a dual-phase grain cluster loaded in uniaxial tension. The results of the simulations are presented and discussed in terms of the effective stress-strain response and the overall deformation anisotropy as functions of the penalty energy parameters. In addition, the prediction of the RGC scheme is compared with predictions using other averaging schemes, as well as to the result of direct finite element (FE) simulation. The comparison indicates that the present RGC scheme is able to approximate FE simulation results of relatively fine discretization at about three orders of magnitude lower computational cost.

Original languageEnglish (US)
Article number015006
JournalModelling and Simulation in Materials Science and Engineering
Volume18
Issue number1
DOIs
StatePublished - 2010
Externally publishedYes

Profile

Carbamyl Phosphate
simulation
Galantamine
Basement Membrane
Grain boundaries
Penalty
penalties
energy
Grain boundary
Finite element simulation
Homogenization
Gradient
Prediction
Term
Energy
Simulation
homogenizing
grain boundaries
gradients
optimization

ASJC Scopus subject areas

  • Modeling and Simulation
  • Condensed Matter Physics
  • Materials Science(all)
  • Mechanics of Materials
  • Computer Science Applications

Cite this

A novel grain cluster-based homogenization scheme. / Tjahjanto, D. D.; Eisenlohr, P.; Roters, F.

In: Modelling and Simulation in Materials Science and Engineering, Vol. 18, No. 1, 015006, 2010.

Research output: Contribution to journalArticle

Tjahjanto, D. D.; Eisenlohr, P.; Roters, F. / A novel grain cluster-based homogenization scheme.

In: Modelling and Simulation in Materials Science and Engineering, Vol. 18, No. 1, 015006, 2010.

Research output: Contribution to journalArticle

@article{1c34f158f58d4744bdf49552eb514f40,
title = "A novel grain cluster-based homogenization scheme",
abstract = "An efficient homogenization scheme, termed the relaxed grain cluster (RGC), for elasto-plastic deformations of polycrystals is presented. The scheme is based on a generalization of the grain cluster concept. A volume element consisting of eight (= 2 × 2 × 2) hexahedral grains is considered. The kinematics of the RGC scheme is formulated within a finite deformation framework, where the relaxation of the local deformation gradient of each individual grain is connected to the overall deformation gradient by the, so-called, interface relaxation vectors. The set of relaxation vectors is determined by the minimization of the constitutive energy (or work) density of the overall cluster. An additional energy density associated with the mismatch at the grain boundaries due to relaxations is incorporated as a penalty term into the energy minimization formulation. Effectively, this penalty term represents the kinematical condition of deformation compatibility at the grain boundaries. Simulations have been performed for a dual-phase grain cluster loaded in uniaxial tension. The results of the simulations are presented and discussed in terms of the effective stress-strain response and the overall deformation anisotropy as functions of the penalty energy parameters. In addition, the prediction of the RGC scheme is compared with predictions using other averaging schemes, as well as to the result of direct finite element (FE) simulation. The comparison indicates that the present RGC scheme is able to approximate FE simulation results of relatively fine discretization at about three orders of magnitude lower computational cost.",
author = "Tjahjanto, {D. D.} and P. Eisenlohr and F. Roters",
year = "2010",
doi = "10.1088/0965-0393/18/1/015006",
volume = "18",
journal = "Modelling and Simulation in Materials Science and Engineering",
issn = "0965-0393",
publisher = "IOP Publishing Ltd.",
number = "1",

}

TY - JOUR

T1 - A novel grain cluster-based homogenization scheme

AU - Tjahjanto,D. D.

AU - Eisenlohr,P.

AU - Roters,F.

PY - 2010

Y1 - 2010

N2 - An efficient homogenization scheme, termed the relaxed grain cluster (RGC), for elasto-plastic deformations of polycrystals is presented. The scheme is based on a generalization of the grain cluster concept. A volume element consisting of eight (= 2 × 2 × 2) hexahedral grains is considered. The kinematics of the RGC scheme is formulated within a finite deformation framework, where the relaxation of the local deformation gradient of each individual grain is connected to the overall deformation gradient by the, so-called, interface relaxation vectors. The set of relaxation vectors is determined by the minimization of the constitutive energy (or work) density of the overall cluster. An additional energy density associated with the mismatch at the grain boundaries due to relaxations is incorporated as a penalty term into the energy minimization formulation. Effectively, this penalty term represents the kinematical condition of deformation compatibility at the grain boundaries. Simulations have been performed for a dual-phase grain cluster loaded in uniaxial tension. The results of the simulations are presented and discussed in terms of the effective stress-strain response and the overall deformation anisotropy as functions of the penalty energy parameters. In addition, the prediction of the RGC scheme is compared with predictions using other averaging schemes, as well as to the result of direct finite element (FE) simulation. The comparison indicates that the present RGC scheme is able to approximate FE simulation results of relatively fine discretization at about three orders of magnitude lower computational cost.

AB - An efficient homogenization scheme, termed the relaxed grain cluster (RGC), for elasto-plastic deformations of polycrystals is presented. The scheme is based on a generalization of the grain cluster concept. A volume element consisting of eight (= 2 × 2 × 2) hexahedral grains is considered. The kinematics of the RGC scheme is formulated within a finite deformation framework, where the relaxation of the local deformation gradient of each individual grain is connected to the overall deformation gradient by the, so-called, interface relaxation vectors. The set of relaxation vectors is determined by the minimization of the constitutive energy (or work) density of the overall cluster. An additional energy density associated with the mismatch at the grain boundaries due to relaxations is incorporated as a penalty term into the energy minimization formulation. Effectively, this penalty term represents the kinematical condition of deformation compatibility at the grain boundaries. Simulations have been performed for a dual-phase grain cluster loaded in uniaxial tension. The results of the simulations are presented and discussed in terms of the effective stress-strain response and the overall deformation anisotropy as functions of the penalty energy parameters. In addition, the prediction of the RGC scheme is compared with predictions using other averaging schemes, as well as to the result of direct finite element (FE) simulation. The comparison indicates that the present RGC scheme is able to approximate FE simulation results of relatively fine discretization at about three orders of magnitude lower computational cost.

UR - http://www.scopus.com/inward/record.url?scp=75649098140&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=75649098140&partnerID=8YFLogxK

U2 - 10.1088/0965-0393/18/1/015006

DO - 10.1088/0965-0393/18/1/015006

M3 - Article

VL - 18

JO - Modelling and Simulation in Materials Science and Engineering

T2 - Modelling and Simulation in Materials Science and Engineering

JF - Modelling and Simulation in Materials Science and Engineering

SN - 0965-0393

IS - 1

M1 - 015006

ER -