Wave Propagation in Nonlinear Viscoelastic Solids

Nunziato, Jace W.; Walsh, E. K.; Schuler, K.W.; Barker, L. M.

doi:10.1007/978-3-642-69571-1_1

Cited by 26 publications

(27 citation statements)

References 138 publications

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“…[17])-is the interaction between nonlinearity and dissipation, in particular, between nonlinearity in the instantaneous response and dissipation due to memory. Single-integral laws, even though relatively simple, capture the essence of this interaction.…”

Section: Jo (13)mentioning

confidence: 99%

On energies for nonlinear viscoelastic materials of single-integral type

Gurtin¹,

Hrusa²

1988

Quart. Appl. Math.

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Section: Jo (13)mentioning

confidence: 99%

On energies for nonlinear viscoelastic materials of single-integral type

Gurtin¹,

Hrusa²

1988

Quart. Appl. Math.

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“…Thus the instantaneous elastic response function may be inferred from measurements of the stress jump across shocks in undeformed materials [1].…”

Section: Single Integral Lawsmentioning

confidence: 99%

“…An example of such a relation was given by Nunziato et al [1] for an acceleration wave propagating into a deformed region in equilibrium in a finite linear viscoelastic solid. 3 They showed that…”

Section: Introductionmentioning

confidence: 99%

“…The front of a ramp wave is an example of an acceleration wave. 1 Expansive (unloading) ramp waves can be generated by reflection of a shock wave from a free surface or a lower impedance material [1]. Compressive ramp waves can be generated by use of fused silica buffer plates or by graded density impactors [1,3] and also by fast pulsed power techniques [3].…”

Section: Introductionmentioning

confidence: 99%

“…In particular, for viscoelastic materials governed by single or multiple integral laws, the dependence of the wave speed on the strain history typically involves an explicit dependence on the relaxation kernel function(s) in the hereditary integral(s). 2 However, for special classes of viscoelastic solids and/or special strain histories, simple explicit formu- 1 More precisely, an acceleration wave is a propagating singular surface across which the stress, strain and particle velocity are continuous but their spatial gradients and time derivatives suffer jump discontinuities [1,2]. 2 See eq.…”

Section: Introductionmentioning

confidence: 99%

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Universal Relations for Acceleration Wave Speeds in Nonlinear Viscoelastic Solids

Scheidler¹

2004

AIP Conference Proceedings

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, ARL-RP-132 SPONSOR/MONITOR'S ACRONYM(S) 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited. ABSTRACTFor finite deformations of nonlinear viscoelastic solids, the speed of propagation of acceleration waves (i.e., ramp waves) generally depends not only on the current state of strain at the wave front but also on the prior strain history. Consequently, explicit formulas for the wave speed can be quite complicated. Simple formulas for the wave speed do exist for special classes of materials and/or special deformation histories, and in this regard we consider one-dimensional motions of viscoelastic solids governed by single integral laws. Some of the relations obtained are universal in the sense that they hold for all materials in a given class and do not explicitly involve the relaxation kernel function in the hereditary integral defining these materials. Abstract. For finite deformations of nonlinear viscoelastic solids, the speed of propagation of acceleration waves (i.e., ramp waves) generally depends not only on the current state of strain at the wave front but also on the prior strain history. Consequently, explicit formulas for the wave speed can be quite complicated. Simple formulas for the wave speed do exist for special classes of materials and/or special deformation histories, and in this regard we consider one-dimensional motions of viscoelastic solids governed by single integral laws. Some of the relations obtained are universal in the sense that they hold for all materials in a given class and do not explicitly involve the relaxation kernel function in the hereditary integral defining these materials. SUBJECT TERMS

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On the use of acceleration waves to characterize the dynamic response of non‐linear viscoelastic materials

Nunziato¹

1978

Polymer Engineering & Sci

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We consider the analysis of data obtained in one-dimensional acceleration wave experiments on a non-linear viscoelastic material and discuss how such data can be used to characterize the dynamic response of the material. To begin, we review briefly the general theory of one-dimensional motions in viscoelastic materials and the methods employed to generate and observe acceleration waves in a material sample. We then discuss two methods of data analysis, a wave front analysis and a wave profile analysis, and indicate the type of information each analysis provides with regard to the dynamic properties of the material. Finally, using a known model for poly(methy1 methacrylate) in a finite-difference, Lagrangian wave-propagation code, we calculate a leration wave profiles at several locations in the sample and, treating these profiles as "experimental" data, we then illustrate how data from three or more acceleration wave experiments can be used to formulate a specific viscoelastic constitutive model for the material.

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Wave Propagation in Nonlinear Viscoelastic Solids

Cited by 26 publications

References 138 publications

On energies for nonlinear viscoelastic materials of single-integral type

On energies for nonlinear viscoelastic materials of single-integral type

Universal Relations for Acceleration Wave Speeds in Nonlinear Viscoelastic Solids

On the use of acceleration waves to characterize the dynamic response of non‐linear viscoelastic materials

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