FINITE-AMPLITUDE INHOMOGENEOUS PLANE WAVES IN A DEFORMED MOONEY-RIVLIN MATERIAL

@article{Destrade2000FINITEAMPLITUDEIP,
  title={FINITE-AMPLITUDE INHOMOGENEOUS PLANE WAVES IN A DEFORMED MOONEY-RIVLIN MATERIAL},
  author={Michel Destrade},
  journal={Quarterly Journal of Mechanics and Applied Mathematics},
  year={2000},
  volume={55},
  pages={109-126}
}
  • M. Destrade
  • Published 1 September 2000
  • Physics
  • Quarterly Journal of Mechanics and Applied Mathematics
The propagation of small-amplitude inhomogeneous plane waves in an isotropic homogeneous incompressible Mooney-Rivlin material is considered when the material is maintained in a state of finite static homogeneous deformation. Disturbances of complex exponential type are sought and all propagating inhomogeneous solutions to the equations of motion are given, as well as the conditions for linear, elliptical, or circular polarization. It is seen that a great variety of solutions arises. These… 
Small-amplitude inhomogeneous plane waves in a deformed Mooney–Rivlin material
The propagation of small-amplitude inhomogeneous plane waves in an isotropic homogeneous incompressible Mooney–Rivlin material is considered when the material is maintained in a state of finite
Superposition of finite- amplitude waves propagating in a principal plane of a deformed Mooney- Rivlin material
Abstract Here we consider finite-amplitude wave motions in Mooney–Rivlin elastic materials which are first subjected to a static homogeneous deformation (prestrain). We assume that the time-dependent
Circularly-polarized plane waves in a deformed Hadamard material
Abstract Small-amplitude inhomogeneous plane waves propagating in any direction in a homogeneously deformed Hadamard material are considered. Conditions for circular polarization are established. The
Superposition of transverse and longitudinal finite-amplitude waves in a deformed Blatz—Ko Material
In this paper, special Blatz—Ko nonlinear elastic materials are considered, which are characterized by a constitutive constant and a constitutive function. We here deal with the propagation of
Circularly polarized plane waves in a deformed Hadamard material
Small-amplitude inhomogeneous plane waves propagating in any direction in a homogeneously deformed Hadamard material are considered. Conditions for circular polarization are established. The analysis
Finite-Amplitude Damped Inhomogeneous Waves in a Deformed Blatz-Ko Material
In this paper special Blatz-Ko nonlinear elastic materials are considered, which are characterized by a constitutive constant and a constitutive function. We deal with the propagation of
Title Circularly-polarized plane waves in a deformed Hadamardmaterial
Small amplitude inhomogeneous plane waves propagating in any direction in a homogeneously deformed Hadamard material are considered. Conditions for circular polarization are established. The analysis
Finite-amplitude inhomogeneous waves in Mooney–Rivlin viscoelastic solids
New exact solutions are exhibited within the framework of finite viscoelasticity. More precisely, the solutions correspond to finite-amplitude, transverse, linearly polarized, inhomogeneous motions
Finite-amplitude inhomogeneous waves in Mooney – Rivlin viscoelastic solids
New exact solutions are exhibited within the framework of finite viscoelasticity. More precisely, the solutions correspond to finite-amplitude, transverse, linearly polarized, inhomogeneous motions
Title Finite amplitude inhomogeneous waves in Mooney-Rivlinviscoelastic solids
New exact solutions are exhibited within the framework of finite viscoelasticity. More precisely, the solutions correspond to finiteamplitude, transverse, linearly-polarized, inhomogeneous motions
...
1
2
...

References

SHOWING 1-10 OF 30 REFERENCES
Finite-amplitude waves in deformed mooney-rivlin materials
In a previous paper (3), Currie and Hayes showed that two linearly polarized finite-amplitude shear waves, polarized in directions orthogonal to each other and to the direction of propagation n, may
Inhomogeneous plane waves
This paper deals with the propagation of elliptically polarised inhomogeneous, time-harmonic plane waves. Such waves arise in many areas. Examples include Rayleigh, Love and Stoneley waves in
Further properties of finiteamplitude plane waves in deformed mooney-rivlin materials
In a previous paper, Currie and Hayes (J. Inst. Maths Applics 5 (1969) 140-161) showed that two linearly polarized finite-amplitude plane shear waves may propagate with constant speeds along any
Finite-Amplitude Inhomogeneous Plane Waves of Exponential Type in Incompressible Elastic Materials
It is proved that elliptically polarized finite-amplitude inhomogeneous plane waves may not propagate in an elastic material subject to the constraint of incompressibility. The waves considered are
Waves in isotropic elastic materials of Hadamard, Green, or harmonic type
Abstract The propagation condition for infinitesimal plane waves superposed on a state of homogeneous strain in isotropic elastic solids is expressed in a simple form in terms of certain
On Surface Waves and Deformations in a Pre-stressed Incompressible Elastic Solid
The propagation of infinitesimal surface waves on a half-space of incompressible isotropic elastic material subject to a general pure homogeneous pre-strain is considered. The secular equation for
The Influence of Initial Stress on Elastic Waves
A rigorous treatment is given of the problem of wave propagation in an elastic continuum when the influence of the initial stress is taken into account. After a short review of the theory various
General theory of small elastic deformations superposed on finite elastic deformations
  • A. Green, R. Rivlin, R. Shield
  • Mathematics
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1952
Using tensor notations a general theory is developed for small elastic deformations, of either a compressible or incompressible isotropic elastic body, superposed on a known finite deformation,
Bivectors and waves in mechanics and optics
The ellipse bivectors complex symmetric matrices complex orthogonal matrices ellipsoids homogenous and inhomogeneous plane waves description of elliptical polarization energy flux electromagnetic
Some dynamic properties of a prestressed incompressible hyperelastic material
  • J. Belward
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 1973
The work continues some earlier investigations into dynamic properties of prestressed incompressible elastic materials. Whereas the material was previously assumed to be a Mooney material, it is here
...
1
2
3
...