Nonlinearity parameters for pulse propagation in isotropic elastomers

Carman, Greg P.; Cramer, M. S.

doi:10.1121/1.402727

Cited by 5 publications

(4 citation statements)

References 12 publications

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“…Now we see that the equations of motion ( 7) are the same whether the choice (8) or the choice ( 9) is made. The two approaches in modeling the dissipative effects are reconciled, at least as far as finite amplitude motions in incompressible materials are concerned.…”

Section: Remark On Finite Amplitude Motions In Incompressible Materialsmentioning

confidence: 92%

“…Chadwick [21, p.146]) thatĖ = F T DF = D in general. Thus we remark, for the time being, that the assumptions (8) and (9) are not equivalent a priori. We discuss these issues further at the end of the next Subsection.…”

Section: Remark On the Dissipative Stress Tensormentioning

confidence: 92%

“…These equations have been developed in the purely elastic case of a single shear wave by Carman and Cramer [8], who determined some numerical and asymptotic solutions.…”

Section: Finite Amplitude Longitudinal and Transverse Plane Wavesmentioning

confidence: 99%

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Finite amplitude elastic waves propagating in compressible solids

Destrade

Saccomandi

2005

Phys. Rev. E

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The paper studies the interaction of a longitudinal wave with transverse waves in general isotropic and unconstrained hyperelastic materials, including the possibility of dissipation. The dissipative term chosen is similar to the classical stress tensor describing a Stokesian fluid and is commonly used in nonlinear acoustics. The aim of this research is to derive the corresponding general equations of motion, valid for any possible form of the strain energy function and to investigate the possibility of obtaining some general and exact solutions to these equations by reducing them to a set of ordinary differential equations. Then the reductions can lead to some exact closed-form solutions for special classes of materials (here the examples of the Hadamard, Blatz-Ko, and power-law strain energy densities are considered, as well as fourth-order elasticity). The solutions derived are in a time-space separable form and may be interpreted as generalized oscillatory shearing motions and generalized sinusoidal standing waves. By means of standard methods of dynamical systems theory, some peculiar properties of waves propagating in compressible materials are uncovered, such as for example, the emergence of destabilizing effects. These latter features exist for highly nonlinear strain energy functions such as the relatively simple power-law strain energy, but they cannot exist in the framework of fourth-order elasticity.

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Section: Remark On Finite Amplitude Motions In Incompressible Materialsmentioning

confidence: 92%

Section: Remark On the Dissipative Stress Tensormentioning

confidence: 92%

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Finite amplitude elastic waves propagating in compressible solids

Destrade

Saccomandi

2005

Phys. Rev. E

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“…One of the peculiarities occurring in polymeric solids is their tolerance to bear large static predeformations without becoming in elastic. An instructive reference is [1], and it is for the ®elds of application described there that the results derived here are most relevant. Applications comprise, for instance, material testing and signal transmission in delay systems.…”

Section: Introductionmentioning

confidence: 97%

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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A general scheme for the derivation of evolution equations describing mixed nonlinearity

Cramer

Sen

1992

Wave Motion

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Nonlinearity parameters for pulse propagation in isotropic elastomers

Cited by 5 publications

References 12 publications

Finite amplitude elastic waves propagating in compressible solids

Finite amplitude elastic waves propagating in compressible solids

Dynamic Poynting coupling

A general scheme for the derivation of evolution equations describing mixed nonlinearity

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