The elusive and fickle viscoelastic Poisson’s ratio and its relation to the elastic-viscoelastic correspondence principle

Hilton, Harry H.

doi:10.2140/jomms.2009.4.1341

Cited by 49 publications

(21 citation statements)

References 48 publications

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“…(10) or (2a), respectively. Of those two equations, the former involves a convolution, whereas the latter does not, which shows that the correspondence principle is not applicable to the creep Poisson's ratio ν c , as already noted by Hilton (2001Hilton ( , 2009Hilton ( , 2011 and Tschoegl et al (2002). Note that Lakes and Wineman (2006) found a relationship between the two Poisson's ratios ν r and ν c that differs from that given in Eq.…”

Section: The Elastic-viscoelastic Correspondence Principlementioning

confidence: 89%

Theoretical and practical differences between creep and relaxation Poisson’s ratios in linear viscoelasticity

Aili¹,

Vandamme

Torrenti³

et al. 2015

Mech Time-Depend Mater

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Poisson's ratio is a well-defined parameter in elasticity. For time-dependent materials, multiple definitions based on the ratios between lateral and axial deformations are available. Here, we focus ourselves on the two most widely used definitions in the time domain, which define time-dependent functions that we call relaxation Poisson's ratio and creep Poisson's ratio. Those two ratios are theoretically different, but are linked in an exact manner through an equation we derive. We show that those two functions are equal at both initial and large times and that their derivatives with respect to time also are. Based on simple rheological models for both the deviatoric and volumetric creep behaviors, we perform a parametric study and show that the difference between those two time-dependent Poisson's ratios can be significant. However, based on creep data available in the literature, we show that, for cementitious materials, this difference can be negligible or not, depending on the case.

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Section: The Elastic-viscoelastic Correspondence Principlementioning

confidence: 89%

Theoretical and practical differences between creep and relaxation Poisson’s ratios in linear viscoelasticity

Aili¹,

Vandamme

Torrenti³

et al. 2015

Mech Time-Depend Mater

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“…Since the correspondence principle has been proven inapplicable when PRs are involved [87] [88] [89], the usual elastic relations for shear and bulk moduli have no viscoelastic counterparts in terms of PRs, i.e. , , 1 2 2 1…”

Section: ( ) ( )mentioning

confidence: 99%

“…None of the five PR categories defined in [87] [88] [89] fit these needed real time prescriptions, nor does the sixth class fit the constraints imposed by (32). Consequently, it would appear that no universal EVCP based on PRs can be rationally deduced or justified.…”

Section: T VI Jj X T X T T X T T X Jmentioning

confidence: 99%

Elastic and Viscoelastic Poisson’s Ratios: The Theoretical Mechanics Perspective

Hilton¹

2017

MSA

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A recent review publication presented an extensive and comprehensive assessment of the phenomenological relations of Poisson's ratios (PRs) to the behavior and responses of contemporary materials under specific loading conditions. The present review and analysis paper is intended as a theoretical mechanics complement covering mathematical and physical modeling of a single original elastic and of six time and process (i.e. path and stress) dependent viscoelastic PR definitions as well as a seventh special path independent one. The implications and consequences of such models on material characterization are analyzed and summarized. Indeed, PRs based on experimentally obtained 2-D strains under distinct creep and/or relaxation processes exhibit radically different time responses for identical material specimen. These results confirm the PR's implicit path dependence in addition to their separate intrinsic time reliance. Such non-uniqueness of viscoelastic PRs renders them unsuitable as universal material descriptors. Analytical formulations and experimental measurements also examine the physical impossibility of instantaneously achieving time independent loads or strains or their rates thus making certain PR definitions based on constant state variables, while mathematically valid, physically unrealistic and unachievable. A newly developed theoretical/experimental protocol for the determination of the time when loading patterns reach stead-state conditions based on strain accelerations demonstrates the capability to measure this time from experimental data. Due to the process dependent PRs, i.e. stress and stress history paths, the non-existence of a unique viscoelastic PR and of a universal elastic-viscoelastic correspondence principle or analogy (EVCP) in terms of PRs is demonstrated. Additionally and independently, the required double convolution integral construction of linear viscoelastic constitutive relations with the inclusion of PRs is cumbersome analytically and computationally needlessly highly CPU intensive. Furthermore, there is no theoretical fundamental hint as to what loading path is required to produce a unique universal viscoelastic PR definition necessary for formulating a PR based constitutive relation or an EVCP protocol. The analysis associated with an additional Class VII viscoelastic PR establishes it as a universal representation which is loading path and strain independent while still remaining time dependent. This Class PR can be the one used if it is desired to express constitutive relations in terms of PRs, subject to the caveat applying to all PR Classes regarding the CPU intensiveness in the time space due to triple product and double convolution integral constitutive relations. However, the use PRs is unnecessary since any set of material behavior can be uniquely and completely defined in terms of only moduli and/or compliances. The mathematical model of instantaneous initial loading paths, based on Heaviside functions, is examined in detail and shown to lead to infinite vel...

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“…The impossibility of formulating an elastic-viscoelastic correspondence principle (analogy) (EVCP) [10,11] based on PRs has been proven by different analytical formulations in [12][13][14]. Yet, publications continue to appear in respectable archival journals which miss the point by either assuming that viscoelastic PRs are constants or that the EVCP applies to PRs or by extending special PR concepts into general regions where they have been proven to be inapplicable or by using all of the above.…”

Section: Introductionmentioning

confidence: 99%

“…The Class III PR definition [12][13][14] as the ratio of two transforms of perpendicular strains has no physical denotation and is less than useful in its time-space inversion counterpart. Furthermore, it can be shown that PRs cannot be part of viscoelastic constitutive relations and that they cannot encompass the EVCP.…”

Section: Introductionmentioning

confidence: 99%

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

Hilton

2011

J Elast

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Detailed new analytical investigations are presented describing the behavior of Class I, II and III viscoelastic Poisson's ratios (PR). Their previously demonstrated dependence on stress-time histories, which lead to the inability to consider them as universal viscoelastic material properties and the incapacity to produce a general elastic-viscoelastic correspondence principle (EVCP) based, is expanded. A new Class VI PR is analytically derived from the viscoelastic constitutive relations in the Fourier transform (FT) space to achieve the proper FT form of the elastic/viscoelastic correspondence principle, i.e., the elastic-viscoelastic analogy. However, even though this PR Class is a pure universal material property function, it still fails to provide a convenient and useful path to a correspondence principle due to its inopportune constitutive form in real time space vis-à-vis a thermodynamic model with equivalent attributes. Consequently, no general EVCP involving PRs can be formulated. The derived Class VI PRs are equivalent to the defined Class III PRs with 1-D loadings (stresses).

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The elusive and fickle viscoelastic Poisson’s ratio and its relation to the elastic-viscoelastic correspondence principle

Cited by 49 publications

References 48 publications

Theoretical and practical differences between creep and relaxation Poisson’s ratios in linear viscoelasticity

Theoretical and practical differences between creep and relaxation Poisson’s ratios in linear viscoelasticity

Elastic and Viscoelastic Poisson’s Ratios: The Theoretical Mechanics Perspective

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

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