In this paper we consider a family of quasi-static evolution problems involving oscillating energies Εε and dissipations Dε. Even though we have separate τ-convergence of Εε and Dε, the τ-limit F of the sum does not agree with the sum of the τ-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 Εε and Dε. This result contributes to the analysis of the interaction between τ-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 / Braides, A.; Cassano, B.; Garroni, A.; Sarrocco, D.. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - 33:2(2016), pp. 309-328. [10.1016/j.anihpc.2014.10.003]
Quasi-static damage evolution and homogenization: A case study of non-commutability
Braides A.;Garroni A.;
2016-01-01
Abstract
In this paper we consider a family of quasi-static evolution problems involving oscillating energies Εε and dissipations Dε. Even though we have separate τ-convergence of Εε and Dε, the τ-limit F of the sum does not agree with the sum of the τ-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 Εε and Dε. This result contributes to the analysis of the interaction between τ-convergence and variational evolution, which has recently attracted much interest both in the framework of energetic solutions and in the theory of gradient flows.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
