Viscoelastic Solids of Exponential Type. I. Minimal Representations and Controllability
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Certain results about state–space representation, minimality and controllability of a linear viscoelastic solid element of exponential type (VSET) are presented. In particular, we prove that VSET can be viewed as materials with finite memory. This is a first part of a plan which will be continued in a next paper, by studying free energies, stability and attractors in viscoelasticity of exponential type.
KeywordsViscoelasticity Continuum Mechanics Controllability
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- Coleman, B, Owen, D 1974A mathematical foundation of thermodynamicsArch. Rational Mech. Anal.541104Google Scholar
- Del Piero, G, Deseri, L 1995Monotonic, completely monotonic, and exponential relaxation functions in linear viscoelasticityQuart. Appl. Math53273300Google Scholar
- Del Piero, G, Deseri, L 1997On the concepts of state and free energy in linear viscoelasticityArch. Rational Mech. Anal138135Google Scholar
- Fabrizio, M, Giorgi, C, Morro, A 1994Free energies and dissipation properties for systems with memoryArch. Rational Mech. Anal.125341373Google Scholar
- Fabrizio, M, Morro, A 1988Viscoelastic relaxation functions compatible with thermodynamicsJ. Elasticity196375Google Scholar
- Fabrizio, M, Morro, A 1992Mathematical Problems in Linear ViscoelasticitySociety for Industrial and Applied Mathematics (SIAM)Philadelphia, PAGoogle Scholar
- Gentili, G 2002Maximum recoverable work, minimum free energy and state space in linear viscoelasticityQuart. Appl. Math.60153182Google Scholar
- Graffi, D, Fabrizio, M 1990On the notion of state for viscoelastic materials of ‘‘rate’’ typeAtti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.83201208Google Scholar
- Noll, W 1972A new mathematical theory of simple materialsArch. Rational Mech. Anal.48150Google Scholar
- Truesdell, C., Noll, W. 1965The non-linear field theories of mechanics Handbuch der Physik, Band III/3Springer-VerlagBerlinGoogle Scholar
- Zabczyk, J. 1992Mathematical Control Theory An IntroductionBirkhäuser Boston Inc.Boston, MAGoogle Scholar