Publication 14-CNA-015
New Insights on Free Energies and Saint-Venant's Principle in Viscoelasticity
Luca Deseri
Group of Solid and Structural Mechanics-DICAM, University of Trento
via Mesiano 77
38123 Trento, Italy
and
Depts of Civil and Env. Eng. and Mechanical Eng.
Carnegie Mellon University,
Porter Hall, 5000 Forbes Av.,
Pittsburgh PA, 15213 USA
and
The Methodist Hospital Research Institute
6565 Fannin St., MS B-490
Houston, TX 77030 USA
deseri@andrew.cmu.edu
G. Gentili
Dipartimento di Matematica
Università di Bologna
Piazza di Porta S. Donato 5, 40127
Bologna, Italy
J. M. Golden
School of Mathematics
Statistics and Computer Science
Dublin Institute of Technology,
Kevin Street, Dublin, 8, Ireland
Abstract: Explicit expressions for the minimum free energy of a linear
viscoelastic material and Noll's definition of state are used here to explore spatial
energy decay estimates for viscoelastic bodies, in the full dynamical case and
in the quasi-static approximation.
In the inertial case, Chirita et al. obtained a certain spatial decay
inequality for a space-time integral over a portion of the body and over a finite
time interval of the total mechanical energy. This involves the work done on
histories, which is not a function of state in general. Here it is shown that for free
energies which are functions of state and obey a certain reasonable property, the
spatial decay of the corresponding space-time integral is stronger than the one involving the
work done on the past history. It turns out that the bound obtained is optimal
for the minimal free energy.
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