On the determination of free energy in linear viscoelastic solids

DOI10.1007/BF01602660zbMath0123.40802MaRDI QIDQ2627096

E. T. Onat, Shlomo Breuer

Publication date: 1964

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

zbMATH Keywords

mechanics of solids

Related Items (33)

Micromechanical model for viscoelastic materials undergoing damage ⋮ Hamiltonian and Lagrangian theory of viscoelasticity ⋮ On the analytic expression of the free energy in linear viscoelasticity ⋮ Variational formulations for the linear viscoelastic problem in the time domain ⋮ Maximum recoverable work and pseudofree energies for a rigid heat conductor ⋮ Fractional characteristic times and dissipated energy in fractional linear viscoelasticity ⋮ On the thermodynamically consistent fractional wave equation for viscoelastic solids ⋮ On the asymptotic behavior of the quasi-static problem for a linear viscoelastic fluid ⋮ On a mathematical framework for the constitutive equations of anisotropic dielectric relaxation ⋮ Hamiltonian Theory of Viscoelasticity ⋮ An explicit formula for the minimum free energy in linear viscoelasticity ⋮ Lagrange identity in linear viscoelasticity ⋮ Free energies for incompressible viscoelastic fluids ⋮ Consequences of non-uniqueness in the free energy of materials with memory ⋮ Nonlinear differential equations with fractional damping with applications to the 1dof and 2dof pendulum ⋮ The decay of spherical waves in a linear viscoelastic solid ⋮ 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 ⋮ Thermo-viscoelastic influences on spherical waves in a linear nonconducting solid ⋮ A new approach to equations with memory ⋮ Formulation of thermodynamically consistent fractional Burgers models ⋮ New estimates for work in linear viscoelasticity ⋮ A proposal concerning the physical rate of dissipation in materials with memory ⋮ Linear non-isothermal viscoelastic solids ⋮ Some properties for viscous fluids with memory ⋮ Fractional-order relaxation laws in nonlinear viscoelasticity ⋮ A nonlinear viscoelastic model: The pseudo-linear model ⋮ Dissipative dynamical systems. I: General theory ⋮ Dissipative dynamical systems. II: Linear systems with quadratic supply rates ⋮ Plane longitudinal waves of small amplitude in a nonlinear viscoelastic material ⋮ The solution polyhedron of the dissipative inequality for relaxation SISO systems ⋮ Asymptotic stability in linear viscoelasticity with supplies ⋮ Free energies and dissipation properties for systems with memory

Cites Work

• Tentative equations for the propagation of stress, strain and temperature fields in viscoelastic solids
• Stress Analysis for Linear Viscoelastic Materials
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