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.

Quasi-static damage evolution and homogenization: A case study of non-commutability / Andrea, Braides; Garroni, Adriana; David, Sarrocco; Cassano, Biagio. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 33:(2016), pp. 309-328. [10.1016/j.anihpc.2014.10.003]

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

GARRONI, Adriana;CASSANO, BIAGIO
2016

Abstract

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.
2016
damage; variational evolution; calculus of variations; homogenization
01 Pubblicazione su rivista::01a Articolo in rivista
Quasi-static damage evolution and homogenization: A case study of non-commutability / Andrea, Braides; Garroni, Adriana; David, Sarrocco; Cassano, Biagio. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 33:(2016), pp. 309-328. [10.1016/j.anihpc.2014.10.003]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/951808
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