The relaxed work from a history H' to a history H is defined as the minimum work required to approach H via a sequence of continuations of H'. I prove three basic properties of the relaxed work: subadditivity, lower semicontinuity with respect to H for fixed H', and two dissipation inequalities. The proofs require the assumption that the relaxed work be bounded from below. It is proved that this assumption is equivalent to a number of statements of thermodynamic type that, in other thermodynamical contexts, need not be equivalent. The surprising coincidence of statements of a different nature suggests, at least for linear viscoelasticity, the idea of a single dissipation postulate. A systematic deduction of a number of consequences of this postulate forms the object of the final part of the paper.

The relaxed work functional in linear viscoelasticity

DEL PIERO, Gianpietro
2004

Abstract

The relaxed work from a history H' to a history H is defined as the minimum work required to approach H via a sequence of continuations of H'. I prove three basic properties of the relaxed work: subadditivity, lower semicontinuity with respect to H for fixed H', and two dissipation inequalities. The proofs require the assumption that the relaxed work be bounded from below. It is proved that this assumption is equivalent to a number of statements of thermodynamic type that, in other thermodynamical contexts, need not be equivalent. The surprising coincidence of statements of a different nature suggests, at least for linear viscoelasticity, the idea of a single dissipation postulate. A systematic deduction of a number of consequences of this postulate forms the object of the final part of the paper.
2004
DEL PIERO, Gianpietro
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in SFERA 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: https://hdl.handle.net/11392/1201110
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 4
social impact