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Homogenisation of a viscoelastic equation with non-periodic coefficients

Published online by Cambridge University Press:  14 November 2011

Maria-Luisa Mascarenhas
Maria-Luisa Mascarenhas
Affiliation:
C.M.A.F., Av. Professor Gama Pinto, 2, 1699 Lisboa codex, Portugal
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Synopsis

The homogenisation of a linearly viscoelastic composite material is performed without any periodicity assumptions and with no restrictions on the initial data. A term of fading memory is evidenced in the expression of the homogenised stress tensor.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 1-2 , 1987 , pp. 143 - 160
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

1Attouch, H.. Variational Convergence of Functionals and Operators, Appl. Math. Ser. (Boston: Pitman, 1984).Google Scholar
2Bensoussan, A., Lions, L. and Papanicolaou, G.. Asymptotic Analysis for Periodic Structures (Amsterdam: North Holland, 1978).Google Scholar
3Boccardo, L. and Murat, F.. Homogénéisation de problèmes quasi-linéaires. Atti del Congresso Studio di Problemi Lineari dell'Analisi Funzionale, Bressanone, pp. 13–51Bologna: Pitagora Editrice, 1982.Google Scholar
4Colombini, F. and Spagnolo, S.. Sur la convergence de solutions d'equations paraboliques. J. Math. Pures Appl. 56 (1977), 263–306.Google Scholar
5Giorgi, E. De and Spagnolo, S.. Sulla convergenza degli integrali dell'energia per operatori ellitici del secondo ordine. Boll. Un. Mat. Ital. 8 (1973), 391–411.Google Scholar
6Duvaut, G. and Lions, J.. Les Inéquations en Mecanique et en Physique (Paris: Dunod, 1972).Google Scholar
7Francfort, G., Leguillon, D. and Suquet, P.. Homogénéisation de milieux viscoelastiques linéaires de Kelvin-Voigt. C. R. Acad. Sci. Paris Sér. I. Math. 296 (1983), 287–290.Google Scholar
8Francfort, G. and Suquet, P.. Homogenization and Mechanical Dissipation in Thermoviscoelasticity. Arch. Rational Mech. Anal, (to appear).Google Scholar
9Mascarenhas, M. L.. A linear homogenization problem with time dependent coefficient. Trans. Amer. Math. Soc. 281 (1984), 179–195.CrossRefGoogle Scholar
10Murat, F.. H-convergence. Séminaire d'Analyse Fonctionnelle et Numérique 1977/78. Alger (multigraphed).Google Scholar
11Murat, F.. Private communication.Google Scholar
12Sanchez-Palencia, E.. Non Homogeneous Media and Vibration Theory. Lecture Notes in Physics 127 (Berlin: Springer, 1980).Google Scholar
13Spagnolo, S.. Una caratterizzazione degli operatori differenziali autoaggiunti del 2° ordini a coefficienti misurabili e limitati. Rend. Sent. Mat. Univ. Padova 39 (1967), 56–64.Google Scholar
14Spagnolo, S.. Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche. Ann. Scuola Norm. Sup. Pisa (3) 22 (1968), 571–597.Google Scholar
15Spagnolo, S.. Convergence in energy for elliptic operators. Numerical Solutions of Partial Differential Equations, III Synspade 1985, ed. Hubbard, (New York: Academic Press, 1976).Google Scholar
16Tartar, L.. Cours Peccot, Collège de France, March 1977 (partially written in [10]).Google Scholar
17Tartar, L.. Quelques remarques sur l'homogénéisation. Functional Analysis and Numerical Analysis. Proceedings of the Japan-France Seminar 1976, ed. Fujita, H.. Japan Society for the Promotion of Science, 1978.Google Scholar
18. Zhikov, V. V., Kozlov, S. M., Oleinik, O. A. and Ngoan, K. T.. Averaging and G-convergence of differential operators. Russian Math. Surveys 34 (1979), 69–147.CrossRefGoogle Scholar