On Rayleigh-type surface waves in an initially stressed incompressible elastic solid

Shams, Moniba; Ogden, Ray W.

doi:10.1093/imamat/hxs070

Cited by 33 publications

(41 citation statements)

References 18 publications

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“…For full details of the constitutive formulation based on invariants, we refer to Shams et al (2011) and Shams and Ogden (2014). Here we provide a summary of the equations that are needed in the following sections.…”

Section: Invariant Formulationmentioning

confidence: 99%

“…Following Shams et al (2011) and Shams and Ogden (2014) it is convenient to update the reference configuration so that it coincides with the configuration corresponding to the finite homogeneous deformation with all incremental quantities treated as functions of x and t instead of X and t. The incremental deformation (displacement) is denoted u and defined by u(x, t) =χ(χ −1 (x), t), and all other updated incremental quantities are identified by a zero subscript. In particular, we haveḞ 0…”

Section: Fṡ +ḟS =ṡmentioning

confidence: 99%

“…By differentiating (43) and (44) for i = 2 with respect to x 1 and eliminatingṗ ,1 using the first component of the equation of motion (as in Shams and Ogden, 2014 for the half-space problem), and similarly forṗ * ,1 , the incremental traction continuity conditions (42) 3,4 are expressed in terms of ψ and its counterpart ψ * for the layer as…”

Section: Plane Incremental Motionsmentioning

confidence: 99%

“…In contrast to the situation of a half-space subject to finite deformation and a pre-stress associated with it through a constitutive law, for materials with an initial stress parallel to the half-space surface, surface waves were analyzed recently by Shams and Ogden (2014) for an incompressible material, and it is an extension of this development to the case of a layered half-space that is the subject of the present paper.…”

Section: Introductionmentioning

confidence: 99%

“…The basic equations required for the study are presented in Section 2, including development of the constitutive law for an initially stressed elastic material in terms of invariants, as described in Shams and Ogden (2014), and its specialization to the case of a plane strain deformation. Section 3 provides the incremental equations of motion based on the theory of linearized incremental deformations superimposed on a finite deformation, and expressions for the elasticity tensor of an initially stressed material are given in general form and then explicitly in the case of plane strain for a general form of strain-energy function.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The effect of initial stress on the propagation of surface waves in a layered half-space

Nam

Merodio

Ogden

et al. 2016

International Journal of Solids and Structures

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In this paper the propagation of small amplitude surface waves guided by a layer with a finite thickness on an incompressible half-space is studied. The layer and half-space are both assumed to be initially stressed. The combined effect of initial stress and finite deformation on the speed of Rayleigh waves is analyzed and illustrated graphically. With a suitable simple choice of constitutive law that includes initial stress, it is shown that in many cases, as is to be expected, the effect of a finite deformation (with an associated pre-stress) is very similar to that of an initial stress (without an accompanying finite deformation). However, by contrast, when the finite deformation and initial stress are considered together independently with a judicious choice of material parameters different features are found that don't appear in the separate finite deformation or initial stress situations on their own.

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Section: Invariant Formulationmentioning

confidence: 99%

Section: Fṡ +ḟS =ṡmentioning

confidence: 99%

Section: Plane Incremental Motionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The effect of initial stress on the propagation of surface waves in a layered half-space

Nam

Merodio

Ogden

et al. 2016

International Journal of Solids and Structures

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Effects of Rayleigh Waves on the Essential Spectrum in Perturbed Doubly Periodic Elliptic Problems

Bakharev

Cardone

Назаров

et al. 2017

Integr. Equ. Oper. Theory

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We give an example of a scalar second order differential operator in the plane with double periodic coefficients and describe its modification, which causes an additional spectral band in the essential spectrum. The modified operator is obtained by applying to the coefficients a mirror reflection with respect to a vertical or horizontal line. This change gives rise to Rayleigh type waves localized near the line. The results are proven using asymptotic analysis, and they are based on high contrast of the coefficient functions.

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Extension, inflation and torsion of a residually stressed circular cylindrical tube

Merodio

Ogden

2015

Continuum Mech. Thermodyn.

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In this paper we provide a new example of the solution of a finite deformation boundaryvalue problem for a residually-stressed elastic body. Specifically, we analyze the problem of the combined extension, inflation and torsion of a circular cylindrical tube subject to radial and circumferential residual stresses and governed by a residual-stress dependent nonlinear elastic constitutive law. The problem is first of all formulated for a general elastic strain-energy function, and compact expressions in the form of integrals are obtained for the pressure, axial load and torsional moment required to maintain the given deformation. For two specific simple prototype strain-energy functions that include residual stress the integrals are evaluated to give explicit closed-form expressions for the pressure, axial load and torsional moment. The dependence of these quantities on a measure of the radial strain is illustrated graphically for different values of the parameters (in dimensionless form) involved, in particular the tube thickness, the amount of torsion and the strength of the residual stress. The results for the two strain-energy functions are compared and also compared with results when there is no residual stress.

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On Rayleigh-type surface waves in an initially stressed incompressible elastic solid

Cited by 33 publications

References 18 publications

The effect of initial stress on the propagation of surface waves in a layered half-space

The effect of initial stress on the propagation of surface waves in a layered half-space

Effects of Rayleigh Waves on the Essential Spectrum in Perturbed Doubly Periodic Elliptic Problems

Extension, inflation and torsion of a residually stressed circular cylindrical tube

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