Quasi-static damage evolution and homogenization: A case study of non-commutability

Braides, Andrea; Cassano, Biagio; Garroni, Adriana; Sarrocco, David

doi:10.1016/j.anihpc.2014.10.003

Braides, Andrea ; Cassano, Biagio ; Garroni, Adriana ; Sarrocco, David

Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 2, pp. 309-328

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Résumé

In this paper we consider a family of quasi-static evolution problems involving oscillating energies $E^{ε}$ and dissipations $D^{ε}$ . Even though we have separate Γ-convergence of $E^{ε}$ and $D^{ε}$ , 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 $E^{ε}$ and $D^{ε}$ . 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.

MR Zbl

DOI : 10.1016/j.anihpc.2014.10.003

Keywords: Quasi-static motion, Homogenization, Gamma-convergence, Commutativity

@article{AIHPC_2016__33_2_309_0,
     author = {Braides, Andrea and Cassano, Biagio and Garroni, Adriana and Sarrocco, David},
     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},
     year = {2016},
     publisher = {Elsevier},
     volume = {33},
     number = {2},
     doi = {10.1016/j.anihpc.2014.10.003},
     zbl = {1338.35027},
     mrnumber = {3465377},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2014.10.003/}
}

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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

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