Surface and interfacial waves and deformations in pre-stressed elastic materials

This thesis is concerned with the effect of pre-stress on the propagation of surface and interfacial waves in elastic materials. Following a review of the classical theory of Rayleigh and Stoneley waves for linear elastic materials we consider first the propagation of infinitesimal surface waves on a half-space of incompressible material subject to a general pure homogeneous pre-stress; the secular equation for propagation along a principal axis of the pre-stess is obtained for a general strain-energy function, and conditions which ensure stability of the underlying pre-stress are derived; the influence of the pre-stress on the existence of surface waves is examined, and the secular equation is analysed in detail for particular deformations and, for a number of specific forms of strain-energy function, numerical results are used to illustrate the dependence of the wave speed on the pre-stress. Necessary and sufficient conditions for the existence of a unique surface wave are obtained. Corresponding results for a compressible material are also derived. The propagation of (Stoneley) interfacial waves along the boundary between two half-spaces of pre-stressed incompressible isotropic elastic material is then examined. The underlying deformation in each half-space corresponds to a pure homogeneous strain with one principal axis of strain normal to the interface and the others having a common orientation. The secular equation governing the wave speed for propagation along a principal axis is obtained in respect of general strain-energy functions. Detailed analysis of the secular equation reveals general sufficient conditions for the existence of a wave and, in particular cases, necessary and sufficient conditions for the existence of a unique interfacial wave. It is also shown that when an interfacial wave exists its speed is greater than that of the least of the Rayleigh wave speeds for the separate half-spaces, paralleling a result from the linear theory. For the special case of quasi-static interfacial deformations (corresponding to vanishing wave speed) an existence criterion is found; moreover, it is shown that inequalities that exclude surface deformations in each half-space also exclude interfacial deformations. Dependence of the above results on the underlying homogeneous deformations and on material parameters is illustrated by numerical results for the neo-Hookean material

Surface Waves in Pre-Stressed Elastic Materials

Abstract not provided

On Love-type waves in a finitely deformed magnetoelastic layered half-space

In this paper, the propagation of Love-type waves in a homogeneously and finitely deformed layered half-space of an incompressible non-conducting magnetoelastic material in the presence of an initial uniform magnetic field is analyzed. The equations and boundary conditions governing linearized incremental motions superimposed on an underlying deformation and magnetic field for a magnetoelastic material are summarized and then specialized to a form appropriate for the study of Love-type waves in a layered half-space. The wave propagation problem is then analyzed for different directions of the initial magnetic field for two different magnetoelastic energy functions, which are generalizations of the standard neo-Hookean and Mooney–Rivlin elasticity models. The resulting wave speed characteristics in general depend significantly on the initial magnetic field as well as on the initial finite deformation, and the results are illustrated graphically for different combinations of these parameters. In the absence of a layer, shear horizontal surface waves do not exist in a purely elastic material, but the presence of a magnetic field normal to the sagittal plane makes such waves possible, these being analogous to Bleustein–Gulyaev waves in piezoelectric materials. Such waves are discussed briefly at the end of the paper

Acute chest pain in an adolescent with cystic fibrosis in September: Would you have thought about this?

International audienceAcute chest pain is common in patients with cystic fibrosis (CF). Here we report the case of an adolescent who suffered acute chest pain in September after an history of acute abdominal pain and fever. The reason for this clinical sceneriao was found to be Coxsackievirus B3, known to be responsible of Bornholm disease, a frequent but under recognized viral myositis. The diagnosis is mainly clinical, but evocating this diagnosis may avoid unnecessary exam

Surface waves in a deformed isotropic hyperelastic material subject to an isotropic internal constraint

An isotropic elastic half space is prestrained so that two of the principal axes of strain lie in the bounding plane, which itself remains free of traction. The material is subject to an isotropic constraint of arbitrary nature. A surface wave is propagated sinusoidally along the bounding surface in the direction of a principal axis of strain and decays away from the surface. The exact secular equation is derived by a direct method for such a principal surface wave; it is cubic in a quantity whose square is linearly related to the squared wave speed. For the prestrained material, replacing the squared wave speed by zero gives an explicit bifurcation, or stability, criterion. Conditions on the existence and uniqueness of surface waves are given. The bifurcation criterion is derived for specific strain energies in the case of four isotropic constraints: those of incompressibility, Bell, constant area, and Ericksen. In each case investigated, the bifurcation criterion is found to be of a universal nature in that it depends only on the principal stretches, not on the material constants. Some results related to the surface stability of arterial wall mechanics are also presented