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Fading memory spaces and approximate cycles in linear viscoelasticity

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Abstract

Fading memory spaces and approximate cycles in linear viscoelasticity RENDICONTI del SEMINARIO MATEMATICO della UNIVERSITÀ DI PADOVA MAURO FABRIZIO ANGELOMORRO Fadingmemory spaces and approximate cycles in linear viscoelasticity Rendiconti del Seminario Matematico della Università di Padova, tome 82 (1989), p. 239-255. <http://www.numdam.org/item?id=RSMUP_1989__82__239_0> © Rendiconti del Seminario Matematico della Università di Padova, 1989, tous droits réservés. L’accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova » (http://rendiconti.math.unipd.it/) implique l’ac- cord avec les conditions générales d’utilisation (http://www.numdam.org/legal. php). Toute utilisation commerciale ou impression systématique est consti- tutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Fading Memory Spaces and Approximate Cycles in Linear Viscoelasticity. MAURO FABRIZIO - ANGELO MORRO (*) SUMMARY - The theory of linear isothermal viscoelasticity is revisited within the context of materials with fading memory. The compatibility with thermodynamics is investigated by considering approximate cycles in a very general sense. As a result, necessary and sufficient conditions, on the relaxation function, for the validity of the second law are derived which emphasize the role of sinusoidal histories. 1. Introduction. When dealing with mathematical problems in linear viscoelasticity, any information on the relaxation function makes the developments handier and leads to more detailed conclusions. This is the essential motivation for a renewed interest into the thermodynamic restric- tions on the relaxation function (see, e.g., [1, 2]) and references therein. It is the purpose of this paper to develop a general thermodynamic analysis of linear viscoelasticity and

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