Interconversion between relaxation modulus and creep compliance for viscoelastic solids
01 Feb 1999-Journal of Materials in Civil Engineering (American Society of Civil Engineers)-Vol. 11, Iss: 1, pp 76-82
TL;DR: In this article, a new approximate interconversion scheme that uses the local log-log slope of the source function is introduced based on the concept of equivalent time determined by rescaling the physical time, which can be interpreted as a shift factor on a logarithmic time axis.
Abstract: 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
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TL;DR: In this article, a bilinear cohesive zone model (CZM) is employed in conjunction with a viscoelastic bulk (background) material to investigate fracture behavior of asphalt concrete.
353 citations
TL;DR: In this article, a power-law series comprising multiple power law terms is used to represent a globally smooth, broadband viscoelastic behavior with minimal impact from local variance in the data.
Abstract: 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...
197 citations
TL;DR: In this article, a 3D finite element (FE) model was developed to predict pavement responses to vehicular loading, incorporating measured tire-pavement contact stresses, continuous moving wheel loading, and hot-mix asphalt (HMA) viscoelastic characteristics.
Abstract: A three-dimensional (3-D) finite element (FE) model was developed to predict pavement responses to vehicular loading. The model incorporates measured tire-pavement contact stresses, continuous moving wheel loading, and hot-mix asphalt (HMA) viscoelastic characteristics. The model was fine-tuned using implicit-dynamic analysis and validated using pavement response from accelerated loading. Two tire configurations (dualtire assembly and wide-base 455 tire) and three full-depth flexible pavement designs (HMA 152 mm, 254 mm, and 420 mm) were used in both FE modeling and accelerated loading tests. The predicted and calculated strain responses at the bottom of HMA were in agreement. Most important, the study shows that vertical shear strain in the upper 76 to 100 mm of the pavement surface is critical for thick pavement and is influenced by the 3-D tire-pavement contact stresses under each tire rib. However, the tensile strain at the bottom of HMA is affected mainly by the total wheel load. The vertical shear s...
143 citations
Cites methods from "Interconversion between relaxation ..."
...In this case, the local slope of the power model can be determined using Equation 2 (11)....
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TL;DR: In this article, a 3D finite element (FE) model was developed to investigate the dynamic responses of thin, flexible pavement under impulsive loading similar to a falling weight deflectometer test.
Abstract: A three-dimensional (3-D) finite element (FE) model was developed to investigate the dynamic responses of thin, flexible pavement under impulsive loading similar to a falling weight deflectometer test. The FE model simulated the hot-mix asphalt (HMA) surface layer as a linear viscoelastic material and considered the cross-anisotropic stress dependent modulus for the unbound base layer. Implicit dynamic analysis was used to consider the effect of inertia on pavement structural responses. Using two thinpavement structures of different HMA layer thicknesses, 76 and 127 mm, the study analyzed the effects of cross-anisotropic stress-dependent aggregate base modulus and dynamic analysis on pavement responses, including surface deflection, tensile strain at the bottom of the HMA layer, deviator stress in the base layer, and compressive strain on top of the subgrade. Results showed that use of the cross-anisotropic stress-dependent modulus for the unbound base layer resulted in greater predicted pavement response...
111 citations
Cites methods from "Interconversion between relaxation ..."
...The HMA relaxation modulus was converted from laboratorydetermined creep compliance test results through an interconversion procedure (22)....
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31 Jul 2002
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References
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Book•
01 Jan 1961
TL;DR: In this article, the authors describe the nature of Viscoelastic behavior of polymeric systems and approximate relations among the linear Viscoels and approximate interrelations among the Viscelastic Functions.
Abstract: The Nature of Viscoelastic Behavior. Illustrations of Viscoelastic Behavior of Polymeric Systems. Exact Interrelations among the Viscoelastic Functions. Approximate Interrelations among the Linear Viscoelastic Functions. Experimental Methods for Viscoelastic Liquids. Experimental Methods for Soft Viscoelastic Solids and Liquids of High Viscosity. Experimental Methods for Hard Viscoelastic Solids. Experimental Methods for Bulk Measurements. Dilute Solutions: Molecular Theory and Comparisons with Experiments. Molecular Theory for Undiluted Amorphous Polymers and Concentrated Solutions Networks and Entanglements. Dependence of Viscoelastic Behavior on Temperature and Pressure. The Transition Zone from Rubberlike to Glasslike Behavior. The Plateau and Terminal Zones in Uncross-Linked Polymers. Cross-Linked Polymers and Composite Systems. The Glassy State. Crystalline Polymers. Concentrated Solutions, Plasticized Polymers, and Gels. Viscoelastic Behavior in Bulk (Volume) Deformation. Applications to Practical Problems. Appendices. Author & Subject Indexes.
12,676 citations
TL;DR: In this article, a nonlinear regression is proposed for the processing and analysis of dynamic mechanical data, where the experimentally determined dynamic moduli,G′(ω) andG″(ω), are converted into a discrete relaxation modulusG(t) and a discrete creep complianceJ(t).
Abstract: A powerful but still easy to use technique is proposed for the processing and analysis of dynamic mechanical data. The experimentally determined dynamic moduli,G′(ω) andG″(ω), are converted into a discrete relaxation modulusG(t) and a discrete creep complianceJ(t). The discrete spectra are valid in a time window which corresponds to the frequency window of the input data. A nonlinear regression simultaneously adjust the parametersg
i
,λ
i
,i = 1,2, ⋯N, of the discrete spectrum to obtain a best fit ofG′, G″, and it was found to be essential that bothg
i
andλ
i
are freely adjustable. The number of relaxation times,N, adjusts during the iterative calculations depending on the needs for avoiding ill-posedness and for improved fit. The solution is insensitive to the choice of initial valuesg
i,0,λ
i,0,N
0. The numerical program was calibrated with the gel equation which gives analytical expressions both in the time and the frequency domain. The sensitivity of the solution was tested with model data which, by definition, are free of experimental error. From the relaxation time spectrum, a corresponding discrete set of parametersJ
0,η, J
d,i
andΛ
i
of the creep complianceJ(t) can then readily be calculated using the Laplace transform.
544 citations
333 citations
TL;DR: In this paper, the creep function for the National Bureau of Standards polyisobutylene at 25°C was calculated from the relaxation function, using the integral equation connecting them, and the calculated function was shown to be correct in its initial slope, to satisfy the inequality φ(t)ψ(t )⩽1 throughout, and to approach satisfactorily the independently determined asymptote.
Abstract: The creep function for the ``National Bureau of Standards'' polyisobutylene at 25°C is calculated from the relaxation function, using the integral equation connecting them. The calculated function is shown to be correct in its initial slope, to satisfy the inequality φ(t)ψ(t)⩽1 throughout, and to approach satisfactorily the independently determined asymptote.
205 citations