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Research Papers

On Thermodynamic Consistency of Homogenization-Based Multiscale Theories

[+] Author and Article Information
Felipe Lopez Rivarola

LMNI-INTECIN (UBA-CONICET),
Facultad de Ingeniería,
Universidad de Buenos Aires,
Av. Las Heras 2214,
Buenos Aires C1127AAR, Argentina
e-mail: flopez@fi.uba.ar

Guillermo Etse

Professor
Department of “Construcciones y Estructuras,”
Facultad de Ingenieria,
Universidad de Buenos Aires,
Buenos Aires C1127AAR, Argentina
e-mail: getse@herrera.unt.edu.ar

Paula Folino

LMNI-INTECIN (UBA-CONICET),
Facultad de Ingeniería,
Universidad de Buenos Aires,
Av. Las Heras 2214,
Buenos Aires C1127AAR, Argentina
e-mail: pfolino@fi.uba.ar

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received November 1, 2016; final manuscript received February 22, 2017; published online May 12, 2017. Assoc. Editor: Peter W. Chung.

J. Eng. Mater. Technol 139(3), 031011 (May 12, 2017) (9 pages) Paper No: MATS-16-1314; doi: 10.1115/1.4036243 History: Received November 01, 2016; Revised February 22, 2017

In this paper, the necessary and sufficient conditions for fulfilling the thermodynamic consistency of computational homogenization schemes in the framework of hierarchical multiscale theories are defined. The proposal is valid for arbitrary homogenization based multiscale procedures, including continuum and discontinuum methods in either scale. It is demonstrated that the well-known Hill–Mandel variational criterion for homogenization scheme is a necessary, but not a sufficient condition for the micro–macro thermodynamic consistency when dissipative material responses are involved at any scale. In this sense, the additional condition to be fulfilled considering that the multiscale thermodynamic consistency is established. The general case of temperature-dependent, higher order elastoplasticity is considered as theoretical framework to account for the material dissipation at micro and macro scales of observation. It is shown that the thermodynamic consistency enforces the homogenization of the nonlocal terms of the finer scale's free energy density; however, this does not lead to nonlocal gradient effects on the coarse scale. Then, the particular cases of local isothermal elastoplasticity and continuum damage are considered for the purpose of the proposed thermodynamically consistent approach for multiscale homogenizations.

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Grahic Jump Location
Fig. 1

Tension–displacement function for crack opening

Grahic Jump Location
Fig. 2

One-dimensional representation of continuum damage-based material behavior

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