Showing papers in "Quarterly Journal of Mechanics and Applied Mathematics in 1992"
92 citations
TL;DR: In this paper, the velocity and pressure in Stokes flow are written in terms of two functions A and B, where A is biharmonic and B is harmonic, and a sphere theorem for non-axisymmetric flow outside or inside a sphere is stated and proved.
Abstract: The velocity and pressure in Stokes flow are written in terms of two functions A and B, where A is biharmonic and B is harmonic. Lamb's (1) general solution of Stokes's equations and Oseen's (2) solution due to a Stokeslet in the presence of a no-slip spherical boundary have the same structure as our representation. Ranger's (3) representation follows as a special case of our result. A sphere theorem for non-axisymmetric flow outside or inside a sphere is stated and proved. Collins's theorem (4) for axisymmetric flow follows as a special case of our theorem. A few illustrative examples are given and in each case the drag and torque on the sphere are calculated.
55 citations
41 citations
TL;DR: In this article, it was shown that two linearly polarized finite-amplitude shear waves, polarized in directions orthogonal to each other and to the direction of propagation n, may propagate along any direction in a Mooney-Rivlin material which is maintained in a state of arbitrary static finite homogeneous deformation.
Abstract: 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 propagate along any direction in a Mooney-Rivlin material which is maintained in a state of arbitrary static finite homogeneous deformation.Here, we recover this result and obtain explicit expressions for the speeds of the two waves in terms of the angles that n makes with special directions, called 'acoustic axes'. These are the only directions such that the two wave speeds are equal. They are determined only by the basic static deformation of the material. There are two such directions if this deformation is triaxial, and one if it is biaxial.Then, it is shown that, although the theory is nonlinear, the superposition of the two waves propagating along any direction is also a solution. In particular, for propagation along an acoustic axis, elliptically and circularly polarized finite-amplitude waves are possible.Finally, the energy flux and energy density of the waves are considered. © 1992 Oxford University Press.
40 citations
TL;DR: In this article, a model of a transversely isotropic elastic solid whose slowness surface has two conical points on the symmetry axis as well as a ring of double points in a plane perpendicular to this axis was obtained.
Abstract: By restricting the elastic constants, a model is obtained of a transversely isotropic elastic solid whose slowness surface has two conical points on the symmetry axis as well as a ring of double points in a plane perpendicular to this axis. The radiation problem for this solid is analysed for the axial displacement component caused by a point axial body force.
28 citations
27 citations
TL;DR: In this article, the stability of a uniform equilibrium state of an unbounded body is examined by studying the nature of plane harmonic wave solutions of governing equations, and the stability is shown to be bounded by the symmetry of the material and the freedom of choice of B.
Abstract: Equations are derived governing an infinitesimal disturbance of a uniform equilibrium state B of an unbounded body. No restriction is placed on the symmetry of the material and the freedom of choice of B allows the presence of an arbitrary homogeneous prestrain. The stability of B is examined by studying the nature of plane harmonic wave solutions of governing equations
27 citations
26 citations
26 citations
TL;DR: In this paper, an asymptotic analysis is carried out in order to calculate the elastostatic field near the tip of a crack for the finite plane deformation of Hadamard materials.
Abstract: SUMMARY An asymptotic analysis is carried out in order to calculate the elastostatic field near the tip of a crack for the finite plane deformation of Hadamard materials. A general body configuration containing a crack and loading conditions is considered. It is shown that the singular field near the crack tip can be obtained by applying a rigid-body rotation with a subsequent parallel translation to a so-called canonical field. The adjective canonical is adopted here to denote the field in which the crack faces open symmetrically, with the most singular term of order A, just resembling the displacement field of the symmetric mode in linear fracture mechanics. No analogy with the antisymmetric mode is possible, and the crack-equilibrium criterion requires only one stress-intensity factor to be known.
25 citations
TL;DR: In this article, the nonlinear elastic response of a class of materials for which the deformation is subject to an internal material constraint described in experiments by James F. Bell on the finite deformation of a variety of metals is investigated.
Abstract: The nonlinear elastic response of a class of materials for which the deformation is subject to an internal material constraint described in experiments by James F. Bell on the finite deformation of a variety of metals is investigated. The purely kinematical consequences of the Bell constraint are discussed, and restrictions on the full range of compatible deformations are presented in geometrical terms. Then various forms of the constitutive equation relating the stress and stretch tensors for an isotropic elastic Bell material are presented. Inequalities on the mechanical response functions are introduced. The importance of these in applications is demonstrated in several examples throughout the paper.
TL;DR: In this paper, a semilinear elliptic equation in a cylinder of variable cross section subject to zero conditions on the lateral boundaries is considered and a second order differential inequality is obtained for an L 2p cross sectional measure of the solution where p is a positive integer.
Abstract: we consider a semilinear elliptic equation in a cylinder of variable cross section subject to zero conditions on the lateral boundaries. A second order differential inequality is obtained for an L 2p cross sectional measure of the solution where p is a positive integer
TL;DR: In this paper, the boundary layer which arises between the parallel flow of fresh and salt groundwater as occurs in vertical aquifers is investigated, caused by small molecular diffusion and transversal dispersion brought about by the porous environment.
Abstract: SUMMARY In this paper we investigate the boundary layer which arises between the parallel flow of fresh and salt groundwater as occurs in vertical aquifers. It is caused by small molecular diffusion and transversal dispersion brought about by the porous environment. A self-similar transformation leads to a variant of the Falkner-Skan equation. Existence, uniqueness and various properties of the solution, such as monotonicity and asymptotic behaviour, are established and the influence of the ratio of molecular diffusion to transversal dispersion is analysed. Some numerical results are presented.
TL;DR: In this paper, the small strain pure bending is treated using finite deformation theory with consistent neglect of higher order terms, and the equation determined by Lamb using shell theory for the shape of the middle surface is found to apply for all width to thickness ratios.
Abstract: The small strain pure bending is treated using finite deformation theory with consistent neglect of higher order terms. The equation determined by Lamb using shell theory for the shape of the middle surface is found to apply for all width to thickness ratios
TL;DR: In this article, the mathematical solution is formulated in terms of Weber Orr transforms, which are then numerically inverted to obtain the solution of the problem of finding the optimal solution.
Abstract: The mathematical solution is formulated in terms of Weber Orr transforms which are then numerically inverted
TL;DR: In this article, the equilibrium problem for a homogeneous, isotropic incompressible, elastic body subject to homogeneous dead loads such that two of the principal Biot stresses are equal in magnitude is studied.
Abstract: We study the equilibrium problem for a homogeneous, isotropic incompressible, elastic body subject to homogeneous dead loads such that two of the principal Biot stresses are equal in magnitude.