Free energies and dissipation properties for systems with memory

DOI10.1007/BF00375062zbMath0806.73006MaRDI QIDQ1322049

Mauro Fabrizio, Claudio Giorgi, Angelo Morro

Publication date: 20 February 1995

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

zbMATH Keywords

second law of thermodynamicstopologyfree-energy functionallinear viscoelastic materialspositive-definitenesscyclic processesdissipation principleBoltzmann modulusconstitutive influence functionFourier-sine transformhistory spaceLyapunov-type propertiesmeterials of single-integral type

Mathematics Subject Classification ID

Thermodynamics in solid mechanics (74A15) Linear constitutive equations for materials with memory (74D05) Nonlinear constitutive equations for materials with memory (74D10)

Related Items (44)

A boundary condition with memory in electromagnetism ⋮ DISSIPATIVITY AND IRREVERSIBILITY OF ELECTROMAGNETIC SYSTEMS ⋮ On the analytic expression of the free energy in linear viscoelasticity ⋮ Internal dissipation, relaxation property, and free energy in materials with fading memory ⋮ Maximum recoverable work and pseudofree energies for a rigid heat conductor ⋮ Thermodynamics of electromagnetic isothermal systems with memory ⋮ Saint-Venant's principle for rigid heat conductors with memory ⋮ Complex systems: Dissipation and reversibility ⋮ Thermodynamic potentials for electromagnetic fields in the ionosphere ⋮ A study of dynamic crack growth in elastic materials using a cohesive zone model ⋮ Saint-Venant's principle in linear viscoelasticity ⋮ Invariant subspace reduction for linear dynamic analysis of finite-dimensional viscoelastic structures ⋮ On the elimination of infinite memory effects on the stability of a nonlinear non-homogeneous rotating body-beam system ⋮ Dynamics of complex bodies with memory and vector-valued microstructure: existence and uniqueness ⋮ Fractional characteristic times and dissipated energy in fractional linear viscoelasticity ⋮ Exponential stabilization of a flexible structure with a local interior control and under the presence of a boundary infinite memory ⋮ Potential method in the linear theory of viscoelastic materials with voids ⋮ Maximum recoverable work in linear thermoelectromagnetism ⋮ Viscoelastic fluids: free energies, differential problems and asymptotic behaviour ⋮ On the theory of viscoelasticity for materials with double porosity ⋮ An explicit formula for the minimum free energy in linear viscoelasticity ⋮ Exponential stabilization of the rotating disk-beam system with an interior infinite memory control: a minimal state framework ⋮ Free energies for incompressible viscoelastic fluids ⋮ The minimum free energy for an electromagnetic conductor ⋮ Thermal convection in a simple fluid with fading memory ⋮ On rigid linear heat conductors with memory ⋮ Free energies in a general non-local theory of a material with memory ⋮ Well posedness for a general boundary condition problem in electromagnetism ⋮ Consequences of non-uniqueness in the free energy of materials with memory ⋮ A viscous boundary condition with memory in linear elasticity ⋮ Maximum recoverable work for a rigid heat conductor with memory ⋮ The concept of a minimal state in viscoelasticity: new free energies and applications to PDEs ⋮ A new approach to equations with memory ⋮ Minimum free energy in linear thermoelectromagnetism ⋮ A proposal concerning the physical rate of dissipation in materials with memory ⋮ A Proposal Concerning the Physical Rate of Dissipation of Materials with Memory: The Non-isothermal Case ⋮ On the exponential decay of the Euler-Bernoulli beam with boundary energy dissipation ⋮ Thermodynamics of a non-simple heat conductor with memory ⋮ Nonisothermal free energies for linear theories with memory ⋮ Asymptotic behavior in linear thermoelasticity ⋮ Viscoelastic solids of exponential type. I: Minimal representations and controllability ⋮ Viscoelastic solids of exponential type. II: Free energies, stability and attractors ⋮ On the spatial behaviour in dynamics of elastic mixtures ⋮ Energy stability for thermo-viscous fluids with a fading memory heat flux

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sul criterio dell'energia per la stabilita di un sistema termomeccanico
• Viscoelastic relaxation functions compatible with thermodynamics
• A mathematical foundation for thermodynamics
• Thermodynamics and stability
• On the thermodynamics of semi-systems with restrictions on the accessibility of states
• Sull'espressione dell'energia libera nei materiali viscoelastici lineari
• Norms and semi-groups in the theory of fading memory
• Dissipative dynamical systems. I: General theory
• On the determination of free energy in linear viscoelastic solids
• On the thermodynamics of viscoelastic materials of single-integral type
• REVERSIBILITY, RECOVERABLE WORK AND FREE ENERGY IN LINEAR VISCOELASTICITY

This page was built for publication: Free energies and dissipation properties for systems with memory