Plate waves in Hadamard materials

Willson, A. J.

doi:10.1007/bf00041135

Cited by 12 publications

(2 citation statements)

References 4 publications

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“…Focusing on neo-Hookean solids (2.23) they showed that the critical stretches are λ cr = 0.666 for tangential equibiaxial compression (λ 1 = λ, λ 2 = λ −2 , λ 3 = λ), λ cr = 0.544 for plane strain compression (λ 1 = λ, λ 2 = λ −1 , λ 3 = 1), and λ cr = 0.444 for normal equibiaxial compression (λ 1 = λ, λ 2 = λ −1/2 , λ 3 = λ −1/2 ). Theirs was a static stability analysis, later also included in a wider dynamical context by Flavin [28], Willson [29], Chadwick and Jarvis [30], Dowaikh and Ogden [12], and , where σ 0 is the real root of σ 3 + σ 2 + 3σ − 1 = 0 (σ 0 = 0.2956). Clearly, in the examples of plane strain and equi-biaxial strain above, the squared wave speed increases when λ increases and decreases when λ decreases.…”

Section: Example: Compressive Stressesmentioning

confidence: 99%

Acoustic waves at the interface of a pre-stressed incompressible elastic solid and a viscous fluid

Otténio

Destrade

Ogden

2007

International Journal of Non-Linear Mechanics

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We analyze the influence of pre-stress on the propagation of interfacial waves along the boundary of an incompressible hyperelastic half-space that is in contact with a viscous fluid extending to infinity in the adjoining half-space.One aim is to derive rigorously the incremental boundary conditions at the interface; this derivation is delicate because of the interplay between the Lagrangian and the Eulerian descriptions but is crucial for numerous problems concerned with the interaction between a compliant wall and a viscous fluid. A second aim of this work is to model the ultrasonic waves used in the assessment of aortic aneurysms, and here we find that for this purpose the half-space idealization is justified at high frequencies. A third goal is to shed some light on the stability behaviour in compression of the solid half-space, as compared with the situation in the absence of fluid; we find that the usual technique of seeking standing waves solutions is not appropriate when the half-space is in contact with a fluid; in fact, a correct analysis reveals that the presence of a viscous fluid makes a compressed neo-Hookean half-space slightly more stable.For a wave travelling in a direction of principal strain, we obtain results for the case of a general (incompressible isotropic) strain-energy function. For a wave travelling parallel to the interface and in an arbitrary direction in a plane of principal strain, we specialize the analysis to the neo-Hookean strain-energy function.

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Section: Example: Compressive Stressesmentioning

confidence: 99%

Acoustic waves at the interface of a pre-stressed incompressible elastic solid and a viscous fluid

Otténio

Destrade

Ogden

2007

International Journal of Non-Linear Mechanics

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“…We exclude consideration of the special case where a = 0, when the material is a 'restricted Hadamard material' [7,8,9,10]. Then, assuming a = 0, it may be shown [4,5] that in order for the Strong Ellipticity conditions to hold, the following inequalities must be valid:…”

Section: Basic Equations 21 Hadamard Materialsmentioning

confidence: 99%