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.
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Andrea Braides, Biagio Cassano, Adriana Garroni, David Sarrocco, Quasi-static damage evolution and homogenization: A case study of non-commutability. Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 2, pp. 309–328DOI 10.1016/J.ANIHPC.2014.10.003