Methods of interconversion between linear viscoelastic material functions. Part I-a numerical method based on Prony series

A bilinear cohesive zone model tailored for fracture of asphalt concrete considering viscoelastic bulk material

A viscoelastic continuum damage model and its application to uniaxial behavior of asphalt concrete

An approach to modeling the mechanical behavior of fiber reinforced and unreinforced plastics with an evolving internal state is described. Intrinsic nonlinear viscoelastic and viscoplastic behavior of the resin matrix is taken into account along with growth of damage. The thermodynamic framework of the method is discussed first. The Gibbs free energy is expressed in terms of stresses, internal state variables (ISVs), temperatureand moisture content. Simplifications are introduced based on physical models for evolution of the ISVs and on experimental observations of thedependence of strain state on stress state and its history. These simplifications include use of master creep functions that account for multiaxial stresses, environmental factors and aging in a reduced time and other scalars. An explicit representation of the strains follows, which isthen specialized to provide three-dimensional homogenized constitutiveequations for transversely isotropic, fiber composites. Experimentalsupport for these equations is briefly reviewed. Finally, physicalinterpretation of some of the constitutive functions is discussed usingresults from a microcracking model as well as molecular rate process andfree volume theories. It is shown that the present thermodynamicformulation leads to a generalized rate process theory that accounts for abroad distribution of thermally activated transformations in polymers.

Nonlinear Viscoelastic and Viscoplastic Constitutive Equations Based on Thermodynamics

This paper presents an interlaboratory test campaign organized by the RILEM 182-PEB Technical Committee. In the campaign, 11 different test methods, comprising uniaxial tension/compression, 2-, 3- and 4-point bending and indirecttension tests, were utilized in order to investigate fatigue characteristics of a dense graded asphalt concrete mixture. The testing conditions specified were sinusoidal excitation at 10Hz and 10°C using controlled strain and stress modes. In total, more than 150 fatigue tests were carried out during the investigation. The fatigue test results were analyzed using both classical as well as continuum damage mechanics approaches. The fatigue test results obtained using the classical fatigue approach are considerably influenced by test type and mode of loading (controlled stress or strain) used. Consequently, this approach has limited use in realistic fatigue characterization of bituminous materials and pavement structures. In contrast to the classical approach, models founded on continuum damage theory may serve to isolate intrinsic fatigue characteristics from the influence of so-called biased effects, which are largely caused by the accelerated laboratory testing. The continuum damage models investigated may constitute steps, towards a rational mechanistic fatigue characterization model, which are important for effective future pavement design.

Fatigue of bituminous mixtures

An efficient method of fitting Prony-series models to viscoelastic experimental data with power-law presmoothing is presented. A direct fitting of a Prony-series function to experimental data without appropriate presmoothing is difficult when the data have significant variance. A power-law series comprising multiple power-law terms is found capable of portraying a globally smooth, broadband viscoelastic behavior with minimal impact from local variance in the data. However, from a computational point of view, a Prony series representation is preferred to a power-law series representation because of the computational efficiency associated with the exponential basis functions of a Prony series. In this paper, a procedure involving presmoothing of experimental data via power-law-series representation followed by fitting of a Prony-series model to the presmoothed data is discussed and illustrated. Discussion focuses on how experimental data with significant variance can be effectively presmoothed through power...

Fitting Prony-Series Viscoelastic Models with Power-Law Presmoothing

A viscoelastic constitutive model for particulate composites with growing damage

Methods of interconversion between relaxation modulus and creep compliance for linear viscoelastic materials are discussed and illustrated using data from asphalt concrete Existing methods of approximate interconversion are reviewed and compared for their approximating schemes A new approximate interconversion scheme that uses the local log-log slope of the source function is introduced The new scheme is based on the concept of equivalent time determined by rescaling the physical time The rescaling factor, which can be interpreted as a shift factor on a logarithmic time axis, is dictated by the local slope of the source function on log-log scales The unknown target function at a given time is obtained by taking the reciprocal of the source function evaluated at an equivalent time Although the method is developed using a mathematical relationship based on the power-law representations of relaxation modulus and creep compliance, the method is not limited to material functions characterized by power-laws but can be applied to general, non-power-law material functions as long as the relevant material behaviors are broadband and smooth on logarithmic scales The new method renders good results especially when the log-log slope of the source function varies smoothly with logarithmic time

Interconversion between relaxation modulus and creep compliance for viscoelastic solids

New analytical procedures for temperature correction of backcalculated asphalt concrete moduli and surface deflections were developed based on the theory of linear viscoelasticity and the time-temperature superposition principle and verified using falling weight deflectometer data and field temperature measurements. The new correction procedures explicitly utilize the thermorheological properties of the asphalt mixture. The resulting temperature-modulus correction factors depend only on the relaxation modulus and time-temperature shift factor of the mixture. The temperature-deflection correction factor depends on both the material properties and the layer thicknesses of the pavement section. Emphasis has been placed on the analytical description of the mixture's thermoviscoelasticity responsible for temperature effects on mixture modulus and pavement deflection. A mechanistic framework for dealing with temperature correction problems for asphalt pavement has been introduced.

S. W. Park

Papers

A viscoelastic continuum damage model and its application to uniaxial behavior of asphalt concrete

Fitting Prony-Series Viscoelastic Models with Power-Law Presmoothing

A viscoelastic constitutive model for particulate composites with growing damage

Interconversion between relaxation modulus and creep compliance for viscoelastic solids

Temperature correction of backcalculated moduli and deflections using linear viscoelasticity and time-temperature superposition