[Approche stochastique aux effets d'échelle pour les matériaux quasi fragile]
Dans ce papier nous présentons une approche stochastique pour modéliser les effets d'échelle des matériaux quasi fragiles. L'ingrédient clef de cette approche réside dans l'utilisation des champs corrélés pour les propriétés matériaux, principale différence par rapport à la théorie de Weibull. Ainsi, un problème stochastique se pose et peut être résolue par la méthode de Monte Carlo. Les résultats obtenus montrent les capacités de ce modèle à retrouver les effets d'échelle compris entre les deux bornes que représentent la mécanique de l'endommagement et la mécanique de la rupture.
In this Note we present a stochastic approach to model size effects in quasi-brittle materials structures. Contrary to Weibull's theory, the key ingredient is the use of correlated random fields in order to describe the material properties. Thus, a stochastic problem has to be solved that we handle using Monte Carlo method. The numerical results show the capability to retrieve size effects in a range between the two classical bounds which are Continuum Damage Mechanics and Linear fracture Mechanics.
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Mot clés : Mécanique des solides numérique, Décomposition de Karhunen–Loève, Matériaux quasi fragiles, Effet d'échelle
@article{CRMECA_2007__335_8_430_0,
author = {Jean-Baptiste Colliat and Martin Hautefeuille and Adnan Ibrahimbegovic and Hermann G. Matthies},
title = {Stochastic approach to size effect in quasi-brittle materials},
journal = {Comptes Rendus. M\'ecanique},
pages = {430--435},
publisher = {Elsevier},
volume = {335},
number = {8},
year = {2007},
doi = {10.1016/j.crme.2007.06.005},
language = {en},
}
TY - JOUR AU - Jean-Baptiste Colliat AU - Martin Hautefeuille AU - Adnan Ibrahimbegovic AU - Hermann G. Matthies TI - Stochastic approach to size effect in quasi-brittle materials JO - Comptes Rendus. Mécanique PY - 2007 SP - 430 EP - 435 VL - 335 IS - 8 PB - Elsevier DO - 10.1016/j.crme.2007.06.005 LA - en ID - CRMECA_2007__335_8_430_0 ER -
%0 Journal Article %A Jean-Baptiste Colliat %A Martin Hautefeuille %A Adnan Ibrahimbegovic %A Hermann G. Matthies %T Stochastic approach to size effect in quasi-brittle materials %J Comptes Rendus. Mécanique %D 2007 %P 430-435 %V 335 %N 8 %I Elsevier %R 10.1016/j.crme.2007.06.005 %G en %F CRMECA_2007__335_8_430_0
Jean-Baptiste Colliat; Martin Hautefeuille; Adnan Ibrahimbegovic; Hermann G. Matthies. Stochastic approach to size effect in quasi-brittle materials. Comptes Rendus. Mécanique, Volume 335 (2007) no. 8, pp. 430-435. doi : 10.1016/j.crme.2007.06.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.06.005/
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