[Une méthode variationnelle incrémentale pour le couplage entre gradient d’endommagement, thermoélasticité et conduction thermique]
In this work, we propose an incremental variational approach to study the coupling between gradient damage, thermoelasticity and heat conduction phenomena. To this end, we first extend the thermodynamics of linear thermoelasticity to incorporate gradient damage phenomena. After carefully introducing the concept of kinetic entropy to describe the interaction between thermoelasticity and heat conduction, this extension is implemented to establish a four-field incremental energy minimization procedure. By considering a suitable kinetic entropy approximation, the latter is then consistently reduced to a three-field (displacement, damage, and absolute temperature) dependency, numerically implemented by means of a staggered optimization algorithm. Applications consisting in a study of the cracking of a plate under thermal shocks are considered. The approach is shown to deliver reliable predictions, based on comparison to available experimental observations which is also provided.
Dans ce travail, nous proposons une approche variationnelle incrémentale pour étudier le couplage entre les phénomènes d’endommagement non local, thermoélasticité et conduction thermique. À cette fin, nous étendons d’abord le cadre thermodynamique de la thermoélasticité linéaire afin d’y intégrer les phénomènes d’endommagement non local. Après avoir soigneusement introduit le concept d’entropie cinétique pour décrire l’interaction entre thermoélasticité et conduction thermique, cette extension est mise en œuvre pour établir une procédure de minimisation de l’énergie incrémentale à quatre champs. En considérant une approximation adaptée de l’entropie cinétique, cette procédure est ensuite réduite de manière cohérente à une dépendance en trois champs (déplacement, endommagement et température absolue), mise en œuvre numériquement au moyen d’un algorithme d’optimisation alternée. Des applications sont proposées, consistant en l’étude de la fissuration d’une plaque soumise à des chocs thermiques. L’approche montre sa capacité à fournir des prédictions fiables, une comparaison avec les observations expérimentales disponibles étant également présentée.
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Mots-clés : Modèle à gradient d’endommagement, thermoélasticité, conduction thermique, formulation fondée sur la thermodynamique, approche variationnelle incrémentale
Banouho Kamagaté 1 , 2 ; Long Cheng 3 ; Radhi Abdelmoula 4 ; Emile Danho 2 ; Djimédo Kondo 1
CC-BY 4.0
@article{CRMECA_2025__353_G1_1063_0,
author = {Banouho Kamagat\'e and Long Cheng and Radhi Abdelmoula and Emile Danho and Djim\'edo Kondo},
title = {An incremental variational method to the coupling between gradient damage, thermoelasticity and heat conduction},
journal = {Comptes Rendus. M\'ecanique},
pages = {1063--1084},
year = {2025},
publisher = {Acad\'emie des sciences, Paris},
volume = {353},
doi = {10.5802/crmeca.325},
language = {en},
}
TY - JOUR AU - Banouho Kamagaté AU - Long Cheng AU - Radhi Abdelmoula AU - Emile Danho AU - Djimédo Kondo TI - An incremental variational method to the coupling between gradient damage, thermoelasticity and heat conduction JO - Comptes Rendus. Mécanique PY - 2025 SP - 1063 EP - 1084 VL - 353 PB - Académie des sciences, Paris DO - 10.5802/crmeca.325 LA - en ID - CRMECA_2025__353_G1_1063_0 ER -
%0 Journal Article %A Banouho Kamagaté %A Long Cheng %A Radhi Abdelmoula %A Emile Danho %A Djimédo Kondo %T An incremental variational method to the coupling between gradient damage, thermoelasticity and heat conduction %J Comptes Rendus. Mécanique %D 2025 %P 1063-1084 %V 353 %I Académie des sciences, Paris %R 10.5802/crmeca.325 %G en %F CRMECA_2025__353_G1_1063_0
Banouho Kamagaté; Long Cheng; Radhi Abdelmoula; Emile Danho; Djimédo Kondo. An incremental variational method to the coupling between gradient damage, thermoelasticity and heat conduction. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 1063-1084. doi: 10.5802/crmeca.325
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