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