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                <term xml:lang="fr"> flambage</term>
                <term xml:lang="fr"> instabilité</term>
                <term xml:lang="fr"> méthode asymptotique numérique</term>
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              <p>On présente dans cet article une modélisation des instabilités dans les matériaux hétérogènes en considérant les approches numériques multi-échelles du premier et du second ordre. Les techniques proposées combinent la méthode des éléments finis multi-échelle (EF2) et la méthode asymptotique nu-mérique (MAN). La méthode EF2 nous permet une grande souplesse quant au choix de la morphologie des microstructures et la MAN nous permet de suivre avec une grande efficacité les branches solutions même complexes et avec un temps de calcul réduit. L'apport de l'homogénéisation du second ordre est mis en lumière au travers un exemple numérique présentant des instabilités au niveau de la microstructure.</p>
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