Propagation of plane waves of finite amplitude in elastic solids

Davison, Lee

doi:10.1016/0022-5096(66)90022-6

Cited by 33 publications

(22 citation statements)

References 7 publications

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“…Finite amplitude shocks in similar settings were addressed by several researchers, whose objectives are different that the objectives in this work. Davison (1966) proposed a theory with admissibility conditions for shocks to obtain general formulas and demonstrated his theory using an example problem. Aboudi and Benveniste (1973) developed a finite difference-based scheme to solve the equations governing impact-induced nonlinear waves.…”

Section: Introductionmentioning

confidence: 99%

“…In the sequel, we employ the theory of Davison (1966) to obtain and analyze explicit solutions for plane waves of finite amplitude in semi-infinite soft materials under different pre-deformations and impacts. We employ the two most prominent constitutive models for soft materials-the compressible neo-Hookean and Gent models-to describe the stress-strain relation (Gent, 1996, Puglisi andSaccomandi, 2015).…”

Section: Introductionmentioning

confidence: 99%

“…Sec. 2 contains the mathematical description of the problem, and its general resolution for smooth and shock wave solutions (Davison, 1966). The generic solution is specialized in Secs.…”

Section: Introductionmentioning

confidence: 99%

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Smooth waves and shocks of finite amplitude in soft materials

Ziv

Gal

2019

Mechanics of Materials

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Recently developed soft materials exhibit nonlinear wave propagation with potential applications for energy trapping, shock mitigation and wave focusing. We address finitely deformed materials subjected to combined transverse and axial impacts, and study the resultant nonlinear waves. We determine the dependency of the induced motion on the impact, pre-deformation and the employed constitutive models. We analyze the neo-Hookean constitutive model and show it cannot capture shear shocks and tensile-induced shocks, in contrast with experimental results on soft materials. We find that the Gent constitutive model predicts that compressive impact may not be sufficient to induce a quasi-pressure shock-yet it may induce a quasi-shear shock, where tensile impact can trigger quasi-pressure shock-and may simultaneously trigger a quasi-shear shock, in agreement with experimental data. We show that the tensile impact must be greater than a calculated threshold value to induce shock, and demonstrate that this threshold is lowered by application of pre-shear.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Smooth waves and shocks of finite amplitude in soft materials

Ziv

Gal

2019

Mechanics of Materials

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“…The theoretical explanation of the Poynting effect of the coupling between shear and stretch, though well established experimentally, remained obscure until some fourty years later Rivlin [11] came up with a theory of torsion that was successful in explaining the Poynting effect as one of ®nite elasticity. Basic work on longitudinal-to-transversal elastic wave coupling was performed in [4], where the classical theory of characteristics was applied to derive simple-wave and shock-wave solutions for Heaviside-type loading and unloading of a semi-in®nite half-space. Recently, nonlinear wave propagation in elastic solids has been the ®eld that ®nds particular interest in polymer physics.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Poynting coupling

Ellermeier

1998

Archive of Applied Mechanics (Ingenieur Archiv)

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Plane wave propagation in a compressible isotropic hyperelastic material is treated. Emphasis is on the Poynting coupling, which is analysed in a linear and a weakly nonlinear approximation for a statically predeformed material. Unidirectional and resonating waves in the material with and without predeformation are described. NotationThe symbols used in this paper are collected here for convenient reference. They are listed roughly in the order of the appearence in the text. uY vY w dimensional/dimensionless displacement components in longitudinal andspace-®xed, and particle-®xed coordinates, fast time, slow times .mass density of undeformed material R Helmholtz free energy density, internal energy per unit volume of undeformed material c L Y c T propagation velocities of in®nitesimal longitudinal and transversal deformation waves of linear elasticity c AE Y c LYT propagation velocities of in®nitesimal deformation waves in a homogeneously pre-strained hyperelastic material c propagation velocity of statically precompressed or pre-expanded hyperelastic material (without preshear) AY BY CY DY E second AY B and third order CY DY E elastic constants aY bY bY k nondimensional elastic constants associated with AY BY DY respectively 0 Y c 0 Y v 0 homogeneous prestrains wave amplitude-ordering parameter m c L ac T n X À t f Y gY hY FY G strain or particle velocity components aY bY c acceleration wave amplitudes a 0 Y b 0 Y c 0 initial (ballistic) acceleration wave amplitudes K a Y KY k bifurcation parameters in acceleration wave problems m aa4 b q nonlinearity parameter VY m transversal and longitudinal excitation displacement amplitude

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“…co-workers (1976, 1977) and Peters and Breazeale (1968). Studies of nonlinear shear waves have been carried out by Chu (1964) and Davison (1966). These latter studies employed the exact method of characteristics to examine the wave families possible in incompressible and compressible materials, respectively.…”

Section: Introductionmentioning

confidence: 99%

Nonlinearity parameters for pulse propagation in isotropic elastomers

Carman

Cramer

1992

The Journal of the Acoustical Society of America

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The propagation of one-dimensional shear waves in isotropic hyperelastic materials is examined. Both compressible and incompressible materials subject to arbitrarily large shear prestrains are considered. The nonlinear evolution equation governing small disturbances on prestrained undisturbed states is derived. The prestrain is seen to change the nonlinearity from the cubic form found in the unstrained case to the stronger quadratic form governed by the conventional Burgers' equation. Additional results include explicit and general expressions for the quadratic and cubic nonlinearity parameters. Numerical estimates are also provided for natural rubber and foamed polyurethane. It is demonstrated that the quadratic nonlinearity parameter does not increase monotonically with prestrain and may actually vanish at nonzero values of the prestrain.

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Propagation of plane waves of finite amplitude in elastic solids

Cited by 33 publications

References 7 publications

Smooth waves and shocks of finite amplitude in soft materials

Smooth waves and shocks of finite amplitude in soft materials

Dynamic Poynting coupling

Nonlinearity parameters for pulse propagation in isotropic elastomers

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