[The variational approach to damage: I. The foundations]
This Note is devoted to the construction of local brittle damage laws. We first justify by the Drucker–Ilyushin postulate to set their formulation within the framework of Generalized Standard Materials. Accordingly, the strain work becomes a state function whose convexity properties are directly related to the hardening or softening properties of the material. Moreover, the evolution problem can be read as a variational problem which is reinforced so that it finally contains the concepts of stability and of energy conservation.
On s'intéresse aux modèles d'endommagement de type fragile où la variable d'endommagement scalaire est régie par une loi à seuil. Considérant ici des modèles locaux, on rappelle que le postulat de Drucker–Ilyushin impose que le modèle soit nécessairement standard, ce qui fournit automatiquement un cadre variationnel à l'écriture du problème d'évolution. On peut alors définir naturellement les concepts de durcissement, d'adoucissement et de stabilité. On aboutit ainsi à une formulation basée sur les trois principes physiques d'irréversibilité, de stabilité et de bilan d'énergie, directement généralisable à des modèles non locaux et se prêtant à un traitement mathématique rigoureux.
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Keywords: Damage, Stability, Variational methods
Kim Pham 1; Jean-Jacques Marigo 2
@article{CRMECA_2010__338_4_191_0, author = {Kim Pham and Jean-Jacques Marigo}, title = {Approche variationnelle de l'endommagement : {I.} {Les} concepts fondamentaux}, journal = {Comptes Rendus. M\'ecanique}, pages = {191--198}, publisher = {Elsevier}, volume = {338}, number = {4}, year = {2010}, doi = {10.1016/j.crme.2010.03.009}, language = {fr}, }
Kim Pham; Jean-Jacques Marigo. Approche variationnelle de l'endommagement : I. Les concepts fondamentaux. Comptes Rendus. Mécanique, Volume 338 (2010) no. 4, pp. 191-198. doi : 10.1016/j.crme.2010.03.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.03.009/
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