Review of Classical Phenomenological Models of Linear Viscoelasticity

From the 1st-orderPhenomenological models ordinaryLinear viscoelasticity differential equations of the MaxwellPhenomenological modelsMaxwell and Voigt–Kelvin modelPhenomenological modelsVoigt–Kelvin units and modified versions, formulations are obtained and physically discussed of the simplest forms of linear viscoelastic behavior under uniaxial tensile stress relaxation, creep and sinusoidal stressing. The physical and mathematical equivalence of the modified MaxwellPhenomenological modelsMaxwell and Voigt–Kelvin models is shown and used to define a standard linear solidStandard linear solid, the paradigm of the linear viscoelastic behavior, with one single characteristic response (relaxation or retardation) time—different but directly related to each other via the elastic constants of the system. Irreversible viscous flowViscous flow is then combined with the viscoelastic response of a standard linear solid to obtain the stress relaxation, creep and storage and loss behavior of what many be called a standard linear liquidStandard linear liquid; the effects of viscous flow are analytically formulated and graphed, and physically discussed. The conventional presentation of linear viscoelasticityLinear viscoelasticity ends with the physical justification and formulation of the spectra of relaxation and retardation times that characterize the behavior of real materials, one of the major subjects of Part II of the book.