no. 2
Quasi-static damage evolution and homogenization: A case study of non-commutability
Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 2, pp. 309-328.

In this paper we consider a family of quasi-static evolution problems involving oscillating energies Eε and dissipations Dε. Even though we have separate Γ-convergence of Eε and Dε, the Γ-limit F of the sum does not agree with the sum of the Γ-limits. Nevertheless, F can still be viewed as the sum of an internal energy and a dissipation, and the corresponding quasi-static evolution is the limit of the quasi-static evolutions related to Eε and Dε. This result contributes to the analysis of the interaction between Γ-convergence and variational evolution, which has recently attracted much interest both in the framework of energetic solutions and in the theory of gradient flows.

DOI : 10.1016/j.anihpc.2014.10.003
Mots clés : Quasi-static motion, Homogenization, Gamma-convergence, Commutativity 
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     title = {Quasi-static damage evolution and homogenization: {A} case study of non-commutability},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {309--328},
     publisher = {Elsevier},
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Braides, Andrea; Cassano, Biagio; Garroni, Adriana; Sarrocco, David. Quasi-static damage evolution and homogenization: A case study of non-commutability. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 2, pp. 309-328. doi : 10.1016/j.anihpc.2014.10.003. http://www.numdam.org/articles/10.1016/j.anihpc.2014.10.003/

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