TY - JOUR

T1 - Homogenization in finite thermoelasticity

AU - Temizer, I.

AU - Wriggers, P.

N1 - Funding information: Support for this work was provided by the German Research Foundation (DFG) under Grant no. WR 19/36-2.

PY - 2010/10/26

Y1 - 2010/10/26

N2 - 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.

AB - 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.

KW - Dissipation criterion

KW - Finite thermoelasticity

KW - Homogenization

KW - Macroscopic tangents

KW - Multiscale analysis

UR - http://www.scopus.com/inward/record.url?scp=78651297068&partnerID=8YFLogxK

U2 - 10.1016/j.jmps.2010.10.004

DO - 10.1016/j.jmps.2010.10.004

M3 - Article

AN - SCOPUS:78651297068

VL - 59

SP - 344

EP - 372

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

SN - 0022-5096

IS - 2

ER -