Journal of Elasticity

, Volume 115, Issue 1, pp 27–46 | Cite as

Thermomechanical Multiscale Constitutive Modeling: Accounting for Microstructural Thermal Effects

  • Pablo J. BlancoEmail author
  • Sebastián M. Giusti


In this work we present a thermomechanical multiscale constitutive model for materials with microstructure. In these materials thermal effects at microscale have an impact on the effective macroscopic stress. As a result, it turns out that the homogenized stress depends upon the macroscopic temperature and its gradient. In order to allow this interplay to be thermodynamically valid, we resort to a macroscopic extended thermodynamics whose elements are derived from the microscopic behavior using homogenization concepts. Hence, the thermodynamics implications of this new class of multiscale models are discussed. A variational approach based on the Hill–Mandel Principle of Macro-homogeneity, and which makes use of the volume averaging concept over a local representative volume element (RVE), is employed to derive the thermal and mechanical equilibrium problems at the RVE level and the corresponding homogenization expressions for the effective heat flux and stress. The material behavior at the RVE level is described through standard phenomenological constitutive models. To sum up, the novel contribution of the model presented here is that it allows to include the microscopic temperature fluctuation field, obtained from the multiscale thermal analysis, in the micro-mechanical problem at the RVE level while keeping thermodynamic consistency.


Multiscale modeling Elasticity tensor Thermal conductivity tensor Thermal expansion tensor Non-standard thermodynamics 

Mathematics Subject Classification

49S05 74A20 74A60 74Q15 



This research was partly supported by ANPCyT (National Agency for Scientific and Technical Promotion) and PID-UTN (Research and Development Program of the National Technological University) of Argentina, under grants N PICT 2010-1259 and PID/IFN 1417, respectively. Also, we received support of the CNPq (Brazilian Research Council) and FAPERJ (Research Foundation of the State of Rio de Janeiro) agencies of Brazil. The support of all these agencies is gratefully acknowledged.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Laboratório Nacional de Computação Científica LNCC/MCTIPetropolisBrazil
  2. 2.Facultad Regional Córdoba UNT/FRC-CONICETUniversidad Tecnológica NacionalCordobaArgentina

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