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Thermodynamic framework for variance-based non-local constitutive models

Article dans une revue avec comité de lecture
Author
ccMAREAU, Charles
211916 Laboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA]

URI
http://hdl.handle.net/10985/22985
DOI
10.1007/s00161-022-01113-8
Date
2022-06-29
Journal
Continuum Mechanics and Thermodynamics

Abstract

The present work deals with the development of a framework dedicated to the construction of constitutive models with non-local internal variables. Such internal variables allow considering the impact of microstructural changes on the current state of a material point. Non-locality is introduced by considering, not only the spatial average, but also the spatial variance of an internal variable in constitutive relations. The proposed framework relies on continuum thermodynamics to construct the set of constitutive equations. Such a framework allows including some information regarding the spatial distribution of internal variables when constructing non-local models for thermomechanical applications. In contrast with gradient-type models, this strategy does not require additional equilibrium equations and boundary conditions. For the purpose of illustration, some numerical examples are presented. According to the numerical results, the proposed framework can be used to circumvent the difficulties associated with excessive spatial localization or to consider size effects.

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