In this paper we consider a family of quasi-static evolution problems involving oscillating energies and dissipations . Even though we have separate Γ-convergence of and , the Γ-limit of the sum does not agree with the sum of the Γ-limits. Nevertheless, 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 and . 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.
@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}, publisher = {Elsevier}, volume = {33}, number = {2}, year = {2016}, doi = {10.1016/j.anihpc.2014.10.003}, zbl = {1338.35027}, mrnumber = {3465377}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2014.10.003/} }
TY - JOUR AU - Braides, Andrea AU - Cassano, Biagio AU - Garroni, Adriana AU - Sarrocco, David TI - Quasi-static damage evolution and homogenization: A case study of non-commutability JO - Annales de l'I.H.P. Analyse non linéaire PY - 2016 SP - 309 EP - 328 VL - 33 IS - 2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2014.10.003/ DO - 10.1016/j.anihpc.2014.10.003 LA - en ID - AIHPC_2016__33_2_309_0 ER -
%0 Journal Article %A Braides, Andrea %A Cassano, Biagio %A Garroni, Adriana %A Sarrocco, David %T Quasi-static damage evolution and homogenization: A case study of non-commutability %J Annales de l'I.H.P. Analyse non linéaire %D 2016 %P 309-328 %V 33 %N 2 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2014.10.003/ %R 10.1016/j.anihpc.2014.10.003 %G en %F AIHPC_2016__33_2_309_0
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, Volume 33 (2016) no. 2, pp. 309-328. doi : 10.1016/j.anihpc.2014.10.003. http://archive.numdam.org/articles/10.1016/j.anihpc.2014.10.003/
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