Homogenization in finite thermoelasticity

authored by: I. Temizer, P. Wriggers
Abstract: A homogenization framework is developed for the finite thermoelasticity analysis of heterogeneous media. The approach is based on the appropriate identifications of the macroscopic density, internal energy, entropy and thermal dissipation. Thermodynamical consistency that ensures standard thermoelasticity relationships among various macroscopic quantities is enforced through the explicit enforcement of the macroscopic temperature for all evaluations of temperature dependent microscale functionals. This enforcement induces a theoretical split of the accompanying micromechanical boundary value problem into two phases where a mechanical phase imposes the macroscopic deformation and temperature on a test sample while a subsequent purely thermal phase on the resulting deformed configuration imposes the macroscopic temperature gradient. In addition to consistently recovering standard scale transition criteria within this framework, a supplementary dissipation criterion is proposed based on alternative identifications for the macroscopic temperature gradient and heat flux. In order to complete the macroscale implementation of the overall homogenization methodology, methods of determining the constitutive tangents associated with the primary macroscopic variables are discussed. Aspects of the developed framework are demonstrated by numerical investigations on model microstructures.
Organisation(s): Institute of Continuum Mechanics
Type: Article
Journal: Journal of the Mechanics and Physics of Solids
Volume: 59
Pages: 344-372
No. of pages: 29
ISSN: 0022-5096
Publication date: 26.10.2010
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Condensed Matter Physics, Mechanics of Materials, Mechanical Engineering
Electronic version(s): https://doi.org/10.1016/j.jmps.2010.10.004 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{f83f12dd504043a3a33064e3a413239f,
title = "Homogenization in finite thermoelasticity",
abstract = "A homogenization framework is developed for the finite thermoelasticity analysis of heterogeneous media. The approach is based on the appropriate identifications of the macroscopic density, internal energy, entropy and thermal dissipation. Thermodynamical consistency that ensures standard thermoelasticity relationships among various macroscopic quantities is enforced through the explicit enforcement of the macroscopic temperature for all evaluations of temperature dependent microscale functionals. This enforcement induces a theoretical split of the accompanying micromechanical boundary value problem into two phases where a mechanical phase imposes the macroscopic deformation and temperature on a test sample while a subsequent purely thermal phase on the resulting deformed configuration imposes the macroscopic temperature gradient. In addition to consistently recovering standard scale transition criteria within this framework, a supplementary dissipation criterion is proposed based on alternative identifications for the macroscopic temperature gradient and heat flux. In order to complete the macroscale implementation of the overall homogenization methodology, methods of determining the constitutive tangents associated with the primary macroscopic variables are discussed. Aspects of the developed framework are demonstrated by numerical investigations on model microstructures.",
keywords = "Dissipation criterion, Finite thermoelasticity, Homogenization, Macroscopic tangents, Multiscale analysis",
author = "I. Temizer and P. Wriggers",
note = "Funding information: Support for this work was provided by the German Research Foundation (DFG) under Grant no. WR 19/36-2.",
year = "2010",
month = oct,
day = "26",
doi = "10.1016/j.jmps.2010.10.004",
language = "English",
volume = "59",
pages = "344--372",
journal = "Journal of the Mechanics and Physics of Solids",
issn = "0022-5096",
publisher = "Elsevier Ltd.",
number = "2",
}