An Acoustoelastic Theory for Surface Waves in Anisotropic Media

1987 ◽  
Vol 54 (1) ◽  
pp. 127-135 ◽  
Author(s):  
G. Thomas Mase ◽  
G. C. Johnson
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Wave Speed ◽  
Transversely Isotropic ◽  
Wave Speeds ◽  
Local Rotation ◽  
Copper Single Crystals ◽  
Cubic Function

A theory for surface waves in an anisotropic material is developed in the framework of acoustoelasticity in which the material’s strain energy density is taken to be a cubic function in the strain. In order to relate the surface wave speeds to the applied stress, a configuration is introduced in which the effect of the local rotation is removed. The development shows that the surface wave speed can be determined from the eigenvalues of a particular real symmetric 2×2 matrix. Numerical results are given for uniaxial loading applied to aluminum and copper single crystals and to an ideal transversely isotropic aggregate of aluminum.

Steady State Motion and Surface Waves

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
Steady State ◽  
Surface Wave ◽  
Surface Waves ◽  
Existence And Uniqueness ◽  
Wave Speed ◽  
Wave Theory ◽  
Two Dimensional ◽  
Elastic Materials ◽  
Steady State Motion ◽  
Anisotropic Elastic

The Stroh formalism for two-dimensional elastostatics can be extended to elastodynamics when the problem is a steady state motion. Most of the identities in Chapters 6 and 7 remain applicable. The Barnett-Lothe tensors S, H, L now depend on the speed υ of the steady state motion. However S(υ), H(υ), L(υ) are no longer tensors because they do not obey the laws of tensor transformation when υ≠0. Depending on the problems the speed υ may not be prescribed arbitrarily. This is particularly the case for surface waves in a half-space where υ is the surface wave speed. The problem of the existence and uniqueness of a surface wave speed in anisotropic materials is the crux of surface wave theory. It is a subject that has been extensively studied since the pioneer work of Stroh (1962). Excellent expositions on surface waves for anisotropic elastic materials have been given by Farnell (1970), Chadwick and Smith (1977), Barnett and Lothe (1985), and more recently, by Chadwick (1989d).

scholarly journals A Pilot Study of Wet Lung Using Lung Ultrasound Surface Wave Elastography in an Ex Vivo Swine Lung Model

2019 ◽  
Vol 9 (18) ◽  
pp. 3923 ◽  
Author(s):  
Xiaoming Zhang ◽  
Boran Zhou ◽  
Alex X. Zhang
Keyword(s):  
Surface Wave ◽  
Pilot Study ◽  
Wave Speed ◽  
Lung Ultrasound ◽  
Ex Vivo ◽  
Lung Model ◽  
Water Volume ◽  
Lung Water ◽  
Wave Speeds ◽  
Lung Sample

Extravascular lung water (EVLW) is a basic symptom of congestive heart failure and other conditions. Computed tomography (CT) is standard method used to assess EVLW, but it requires ionizing radiation and radiology facilities. Lung ultrasound reverberation artifacts called B-lines have been used to assess EVLW. However, analysis of B-line artifacts depends on expert interpretation and is subjective. Lung ultrasound surface wave elastography (LUSWE) was developed to measure lung surface wave speed. This pilot study aimed at measureing lung surface wave speed due to lung water in an ex vivo swine lung model. The surface wave speeds of a fresh ex vivo swine lung were measured at 100 Hz, 200 Hz, 300 Hz, and 400 Hz. An amount of water was then filled into the lung through its trachea. Ultrasound imaging was used to guide the water filling until significant changes were visible on the imaging. The lung surface wave speeds were measured again. It was found that the lung surface wave speed increases with frequency and decreases with water volume. These findings are confirmed by experimental results on an additional ex vivo swine lung sample.

True bounds on Poisson's ratios for transversely isotropic solids

1992 ◽  
Vol 27 (1) ◽  
pp. 43-44 ◽  
Author(s):  
P S Theocaris ◽  
T P Philippidis
Keyword(s):  
Energy Density ◽  
Basic Principle ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Linear Elastic ◽  
Positive Strain ◽  
Transversely Isotropic Solids ◽  
Isotropic Solids

The basic principle of positive strain energy density of an anisotropic linear or non-linear elastic solid imposes bounds on the values of the stiffness and compliance tensor components. Although rational mathematical structuring of valid intervals for these components is possible and relatively simple, there are mathematical procedures less strictly followed by previous authors, which led to an overestimation of the bounds and misinterpretation of experimental results.

A Geometrically Exact Rod Model Including In-Plane Cross-Sectional Deformation

2010 ◽  
Vol 78 (1) ◽  
Author(s):  
Ajeet Kumar ◽  
Subrata Mukherjee
Keyword(s):  
Energy Density ◽  
Cross Section ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Three Dimensional ◽  
Rigid Motion ◽  
Transversely Isotropic ◽  
Equilibrium Equations ◽  
Cross Sectional ◽  
Deformation Problem

We present a novel approach for nonlinear, three dimensional deformation of a rod that allows in-plane cross-sectional deformation. The approach is based on the concept of multiplicative decomposition, i.e., the deformation of a rod’s cross section is performed in two steps: pure in-plane cross-sectional deformation followed by its rigid motion. This decomposition, in turn, allows straightforward extension of the special Cosserat theory of rods (having rigid cross section) to a new theory allowing in-plane cross-sectional deformation. We then derive a complete set of static equilibrium equations along with the boundary conditions necessary for analytical/numerical solution of the aforementioned deformation problem. A variational approach to solve the relevant boundary value problem is also presented. Later we use symmetry arguments to derive invariants of the objective strain measures for transversely isotropic rods, as well as for rods with inbuilt handedness (hemitropy) such as DNA and carbon nanotubes. The invariants derived put restrictions on the form of the strain energy density leading to a simplified form of quadratic strain energy density that exhibits some interesting physically relevant coupling between the different modes of deformation.

scholarly journals ON SURFACE WAVES IN A FINITELY DEFORMED MAGNETOELASTIC HALF-SPACE

2011 ◽  
Vol 03 (04) ◽  
pp. 633-665 ◽  
Author(s):  
P. SAXENA ◽  
R. W. OGDEN
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Wave Speed ◽  
Sagittal Plane ◽  
Isotropic Energy ◽  
Surface Wave Propagation ◽  
Homogeneous Strain

Rayleigh-type surface waves propagating in an incompressible isotropic half-space of nonconducting magnetoelastic material are studied for a half-space subjected to a finite pure homogeneous strain and a uniform magnetic field. First, the equations and boundary conditions governing linearized incremental motions superimposed on an initial motion and underlying electromagnetic field are derived and then specialized to the quasimagnetostatic approximation. The magnetoelastic material properties are characterized in terms of a "total" isotropic energy density function that depends on both the deformation and a Lagrangian measure of the magnetic induction. The problem of surface wave propagation is then analyzed for different directions of the initial magnetic field and for a simple constitutive model of a magnetoelastic material in order to evaluate the combined effect of the finite deformation and magnetic field on the surface wave speed. It is found that a magnetic field in the considered (sagittal) plane in general destabilizes the material compared with the situation in the absence of a magnetic field, and a magnetic field applied in the direction of wave propagation is more destabilizing than that applied perpendicular to it.

The behaviour of elastic surface waves polarized in a plane of material symmetry. I. Addendum

1991 ◽  
Vol 433 (1889) ◽  
pp. 699-710 ◽  
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Plane Waves ◽  
Transversely Isotropic ◽  
Point Of View ◽  
Reference Plane ◽  
Material Symmetry ◽  
Reflected Waves ◽  
Inhomogeneous Plane ◽  
Symmetric Surface

This addition to a recent paper by Chadwick ( Proc. R. Soc. Lond . A 430, 213 (1990); hereafter referred to as part I) has been prompted mainly by the discovery of secluded supersonic surface waves propagating in configurations of transversely isotropic elastic media in which the reference plane is not a plane of material symmetry and coexisting with a subsonic surface wave. The occurrence of a supersonic surface wave travelling in a direction e 1 with speed v s implies that there are two homogeneous plane waves, with slowness vectors s i and s r such that s i . e 1 = S r . e 1 = v -1 s , which comprise the incident and reflected waves in a case of simple reflection at the traction-free boundary. Supersonic surface waves may therefore be found by searching within a suitably defined space of simple reflection, R . This is the approach which has led to the new results mentioned above and the principal conclusions of part I are re-examined here from the same point of view. It is found that, whereas the secluded supersonic surface waves in transversely isotropic media correspond to isolated points on a curvilinear projection of R which does not intersect the curve representing subsonic surface waves, the symmetric surface waves studied in part I define a curve which may lie partly inside and partly outside a projection of R in the form of a region, the interior points representing supersonic and the exterior points subsonic surface waves. This discussion is preceded by a simplification of the existence-uniqueness theorem proved in part I and followed by a reconsideration of the possibility that an inhomogeneous plane elastic wave can qualify as a surface wave. Such one-component surface waves do exist, but a symmetric surface wave necessarily contains two inhomogeneous plane waves.

scholarly journals Surface waves guided by topography in an anisotropic elastic half-space

2013 ◽  
Vol 469 (2149) ◽  
pp. 20120371 ◽  
Author(s):  
Y. B. Fu ◽  
G. A. Rogerson ◽  
W. F. Wang
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Wave Speed ◽  
Elastic Half Space ◽  
Simple Eigenvalue ◽  
Plane Shear ◽  
Number Of Factors ◽  
Present Context ◽  
Anisotropic Elastic

We consider the propagation of free surface waves on an elastic half-space that has a localized geometric inhomogeneity perpendicular to the direction of wave propagation (such waves are known as topography-guided surface waves). Our aim is to investigate how such a weak inhomogeneity modifies the surface-wave speed slightly. We first recover previously known results for isotropic materials and then present additional results for a generally anisotropic elastic half-space assuming only one plane of material symmetry. It is shown that a topography-guided surface wave in the present context may or may not propagate depending on a number of factors. In particular, they cannot propagate if the original two-dimensional surface wave on a flat half-space is supersonic with respect to the speed of anti-plane shear waves. For the case when a topography-guided surface wave may exist, the existence and computation of wave speed correction is reduced to the solution of a simple eigenvalue problem whose properties are previously well understood. As a by-product of our analysis, we deduce that there exists at least one topography-guided surface wave on an isotropic elastic half-space, and that it is unique when the geometric inhomogeneity has sufficiently small amplitude.

Mechanical Behavior Modeling of Hyperelastic Transversely Isotropic Materials Based on a New Polyconvex Strain Energy Function

2018 ◽  
Vol 10 (09) ◽  
pp. 1850104 ◽  
Author(s):  
D. M. Taghizadeh ◽  
H. Darijani
Keyword(s):  
Energy Density ◽  
Mechanical Behavior ◽  
Test Data ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Transversely Isotropic ◽  
Material Behavior ◽  
Isotropic Materials ◽  
Proposed Model ◽  
Transversely Isotropic Materials

In this paper, the mechanical behavior of incompressible transversely isotropic materials is modeled using a strain energy density in the framework of Ball’s theory. Based on this profound theory and with respect to physical and mathematical aspects of deformation invariants, a new polyconvex constitutive model is proposed for the mechanical behavior of these materials. From the physical viewpoint, it is assumed that the proposed model is additively decomposed into three parts nominally representing the energy contributions from the matrix, fiber and fiber–matrix interaction where each of the parts should be presented in terms of the invariants consistent with the physics of the deformation. From the mathematical viewpoint, the proposed model satisfies the fundamental postulates on the form of strain energy density, specially polyconvexity and coercivity constraints. Indeed, polyconvexity ensures ellipticity condition, which in turn provides material stability and in combination with coercivity condition, guarantees the existence of the global minimizer of the total energy. In order to evaluate the performance of the proposed strain energy density function, some test data of incompressible transverse materials with pure homogeneous deformations are used. It is shown that there is a good agreement between the test data and the obtained results from the proposed model. At the end, the performance of the proposed model in the prediction of the material behavior is evaluated rather than other models for two representative problems.

The behaviour of elastic surface waves polarized in a plane of material symmetry II. Monoclinic media

1992 ◽  
Vol 438 (1902) ◽  
pp. 207-223 ◽  
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Transversely Isotropic ◽  
Reference Plane ◽  
Material Symmetry ◽  
Elastic Surface ◽  
Definite Integrals ◽  
Surface Wave Propagation ◽  
Symmetric Surface ◽  
Speed Of Propagation

A general analysis has been given in part I of symmetric elastic surface waves, characterized by the coincidence of the reference plane with a plane of material symmetry. There follows here a detailed account of the propagation of such waves in media with monoclinic, the minimum type of symmetry. The three definite integrals involved in the determination of the surface-wave function, and hence the speed of propagation, are evaluated and an explicit formula is obtained connecting a fourth integral, also required in the calculation of surface-wave properties, to the other three. Illustrative numerical results are presented, referring in all to 12 monoclinic crystals. The continuous transitions between subsonic and supersonic surface-wave propagation, encountered previously in cubic and transversely isotropic elastic media, occur in seven of the materials and thus emerge as a customary feature of symmetric surface waves. Computations of the associated displacement and traction fields and the paths of particles in the boundary of the transmitting body are also described.

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