The model of dissipation based on memory introduced by Caputo is generalized and checked with experimental dissipation curves of various materials

A new dissipation model based on memory mechanism

SUMMARY This paper is concerned with the development of a computational algorithm for the solution of the uncoupled, quasi-static boundary value problem for a linear viscoelastic solid undergoing thermal and mechanical deformation. The method evolves from a finite element discretization of a stationary value problem, leading to the solution of a system of linear integral equations determining the motion of the solid. An illustrative example is included.

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Thermomechanical analysis of viscoelastic solids

Essay on uncertainties in elastic and viscoelastic structures: From A. M. Freudenthal's criticisms to modern convex modeling

The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the Caputo sense. After giving a necessary outline of the classical theory of linear viscoelasticity, we contrast these two types of fractional derivatives in their ability to take into account initial conditions in the constitutive equations of fractional order. We also provide historical notes on the origins of the Caputo derivative and on the use of fractional calculus in viscoelasticity.

Time-fractional derivatives in relaxation processes: a tutorial survey

Traditionally, various forms of shift factors such as Arrhenius, Williams-Landel-Ferry (WLF), and polynomials have been used with asphalt materials. Shift factors have also been estimated with binder viscosity parameters. Successful extrapolation of viscoelastic functions requires a robust form of shift factor-temperature relationship. This form is important for performing calculations at the extremes of temperature found in practice. A preliminary analysis of complex modulus E* data of mixtures obtained from the Mechanistic-Empirical Pavement Design Guide (MEPDG) database demonstrated that the Kaelble form of shift factor could describe the functional form of the shift factor more accurately than the Arrhenius, WLF, or polynomial-fitting functions. However, the Kaelble shift function as originally described uses the same temperature as a reference temperature and as an inflection temperature. This factor creates a problem when attempts are made to implement the function in a design method or when materia...

R. L. Taylor

Papers

Creep and relaxation