A general closed expression is given for the isothermal minimum free energy of a linear viscoelastic material with continuous spectrum response. Two quite distinct approaches are adopted, which give the same final result. The first involves expressing a positive quantity, closely related to the loss modulus of the material, defined on the frequency domain, as a product of two factors with specified analyticity properties. The second is the continuous spectrum version of a method used in [S. Breuer and E. T. Onat, Z. Angew. Math. Phys., 15 (1964), pp. 13–21] for materials with relaxation function given by sums of exponentials. It is further shown that minimal energy states are uniquely related to histories and that the work function is the maximum free energy with the property that it is a function of state.

The Minimum Free Energy for Continuous Spectrum Materials / Deseri, Luca; M., Golden. - In: SIAM JOURNAL ON APPLIED MATHEMATICS. - ISSN 0036-1399. - STAMPA. - 67:3(2007), pp. 869-892.

The Minimum Free Energy for Continuous Spectrum Materials

Deseri, Luca;
2007

Abstract

A general closed expression is given for the isothermal minimum free energy of a linear viscoelastic material with continuous spectrum response. Two quite distinct approaches are adopted, which give the same final result. The first involves expressing a positive quantity, closely related to the loss modulus of the material, defined on the frequency domain, as a product of two factors with specified analyticity properties. The second is the continuous spectrum version of a method used in [S. Breuer and E. T. Onat, Z. Angew. Math. Phys., 15 (1964), pp. 13–21] for materials with relaxation function given by sums of exponentials. It is further shown that minimal energy states are uniquely related to histories and that the work function is the maximum free energy with the property that it is a function of state.
3
Deseri, Luca; M., Golden
The Minimum Free Energy for Continuous Spectrum Materials / Deseri, Luca; M., Golden. - In: SIAM JOURNAL ON APPLIED MATHEMATICS. - ISSN 0036-1399. - STAMPA. - 67:3(2007), pp. 869-892.
File in questo prodotto:
File Dimensione Formato  
SIAM_2007.pdf

Solo gestori archivio

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 218.02 kB
Formato Adobe PDF
218.02 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/71347
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 15
  • ???jsp.display-item.citation.isi??? 16
social impact