Clarifications of Certain Ambiguities and Failings of Poisson’s Ratios in Linear Viscoelasticity

Hilton, Harry H.

doi:10.1007/s10659-010-9296-z

Cited by 39 publications

(7 citation statements)

References 18 publications

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“…These isotropic constitutive relations—and in the next section their anisotropic cousins—are cast in the form of relaxation and/or creep functions, rather than combinations of the latter and viscoelastic Poisson’s ratios (PR). This is due to the fact viscoelastic PRs have been shown to be intrinsic functions of time [ 42 , 43 , 44 ], stresses and loading conditions and not “pure” material properties such as relaxation functions or moduli [ 45 , 46 , 47 , 48 ].…”

Section: Discussionmentioning

confidence: 99%

Generalized Fractional Derivative Anisotropic Viscoelastic Characterization

Hilton

2012

Materials

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Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and examined in terms of many parameter generalized Kelvin models and are analytically extended to cover general anisotropic homogeneous or non-homogeneous as well as functionally graded viscoelastic material behavior. Equivalent integral constitutive relations, which are computationally more powerful, are derived from fractional differential ones and the associated anisotropic temperature-moisture-degree-of-cure shift functions and reduced times are established. Approximate Fourier transform inversions for fractional derivative relations are formulated and their accuracy is evaluated. The efficacy of integer and fractional derivative constitutive relations is compared and the preferential use of either characterization in analyzing isotropic and anisotropic real materials must be examined on a case-by-case basis. Approximate protocols for curve fitting analytical fractional derivative results to experimental data are formulated and evaluated.

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Section: Discussionmentioning

confidence: 99%

Generalized Fractional Derivative Anisotropic Viscoelastic Characterization

Hilton

2012

Materials

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“…Note that, contrary to valid elastic PR relations, viscoelastic Poisson's ratios do not appear here since the elastic-viscoelastic correspondence principle does not apply to PRs [10] . The symbol λ is Lamé constant and the qualities enclosed in curly brackets,{ }, can be expressed directly in the time space without executing formal inversions, i.e.…”

Section: Direct Determination Of Shear and Bulk Relaxation Modulimentioning

confidence: 96%

“…The f i (t) functions in Eqs. (9) and (10) are assumed the meet the end conditions listed in Table 1 and then curve fitted to the appropriate data in the interval 0 ≤ t ≤ t 1 [1].…”

Section: Constitutive Relations For Viscoelastic Uni-directional Tensmentioning

confidence: 99%

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Characterization of Isotropic Viscoelastic Moduli and Compliances from 1-D Tension Experiments

Michaeli

Shtark²,

Grosbein³

et al. 2012

53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

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The objective is to formulate numerical implementations of analytical and experimental protocols to determine linear viscoelastic material properties without using Poisson's ratios, as devised in [1 -4]. The presented analysis is in terms of 3-D generalized viscoelastic constitutive relations with hereditary integrals and relaxation moduli or creep compliances. The numerical procedures are based on experimental data from photogrammetric and tensile testing instrumentations, which provide stress data in the 1-D loaded direction and strains in both longitudinal and transverse directions. Measurements and data analyses include the entire time range of starting transient and steady-state loading conditions. Experimental data conclusively demonstrates that the loading build up on several versions of INSTRON™ testing machines is sufficiently slow to render unrealistic any analyses based on instantaneous loading models. Consistency relations among the various sets of relaxation times are derived and it is shown that in an isotropic medium the only independent ones are those belonging to shear and bulk moduli. Some relaxation moduli are obtainable directly from the shear and bulk ones in the time space while other moduli and compliances can only be determined through Fourier or Laplace transforms of the former.

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“…Correspondence Principle (EVCP) cannot be utilized in the determination of the PR of viscoelastic materials due to its dependence on its loading history [21][22][23] . In order to describe the time-dependent response without the use of the PR, it is necessary to obtain any two of the three isotropic material properties that include Young's, shear, and bulk relaxation moduli and/or creep compliances or their corresponding relaxation and/or creep functions.…”

Section: Pr Of Viscoelastic Materialsmentioning
confidence: 99%

Statistical Analysis of Viscoelastic Creep Compliance of Vinyl Ester Resin
Simsiriwong
¹
,
Sullivan
²
,
Hilton
³

et al. 2012
53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
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The objective of this study is to formulate the statistical distribution functions for the viscoelastic creep compliance of a vinyl ester polymer. Short-term tensile creep/creep recovery experiments are conducted at two stress levels and at three temperatures below the glass transition temperature. Strain measurements in the longitudinal and transverse directions are measured simultaneously using the digital image correlation technique. The creep compliance functions are obtained using the generalized 3-D viscoelastic constitutive equation with a Prony series representation. Weibull and lognormal distributions are considered for the probability distribution of the creep functions. This effort involves an analytical study based on experimental results for representing the data scatter in polymer composites. Such a study has not been found in the literature. Nomenclature ε ii (t)= sampled strain at t σ jj (t) = sampled stress at t C 0 iijj = elastic compliance C n iijj = Prony series coefficient C iijj (t) = creep compliance at t τ n = retardation time N pr = length of Prony series (1≤ n ≤ Npr) t 1 = time when load reaches steady state (t 1 > 0) H(t) = Heaviside step function t m * = the m th experimental time sample β = Weibull shape parameter α = Weibull scale parameter μ = Lognormal mean parameter σ = Lognormal standard deviation parameter 2 N 0 = number of sample size D no = Kolmogorov-Smirnov maximum deviation λ = Significance level ν ij (t) = Poisson's ratio at t

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Clarifications of Certain Ambiguities and Failings of Poisson’s Ratios in Linear Viscoelasticity

Cited by 39 publications

References 18 publications

Generalized Fractional Derivative Anisotropic Viscoelastic Characterization

Generalized Fractional Derivative Anisotropic Viscoelastic Characterization

Characterization of Isotropic Viscoelastic Moduli and Compliances from 1-D Tension Experiments

Statistical Analysis of Viscoelastic Creep Compliance of Vinyl Ester Resin

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