A unified framework for coupled Navier-Stokes/Cahn-Hilliard equations is developed using, as a basis, a balance law for microforces in conjunction with constitutive equations consistent with a mechanical version of the second law.As a numerical application of the theory, we consider the kinetics of coarsening for a binary fluid in two space-dimensions.

Cavitation phenomena in nonlinearly elastic solids have been the subject of extensive investigation in recent years. The impetus for much of these theoretical developments has been supplied by pioneering work of Ball in 1982. Ball investigated a class of bifurcation problems for the equations of nonlinear elasticity which model the appearance of a cavity in the interior of an apparently solid homogensous isotropic elastic sphere or cylinder once a critical external tensile load is attained. This model may also be interpreted in terms of the sudden rapid growth of a pre-existing microvoid. In this paper, we briefly summarize some of the main results obtained to date on radially symmetric cavitation, using the bifurcation model. The paper is a review and a comprehensive list of references is given to original work where details of the analyses may be found.

In this paper, the effect of material anisotropy on void nucleation and growth in incompressible nonlinearly elastic solids is examined. A bifurcation problem is considered for a solid sphere composed of an incompressible homogeneous nonlinearly elastic material which is transversely isotropic about the radial direction. Under a uniform radial tensile dead-load, a branch of radially symmetric configurations involving a traction-free internal cavity bifurcates from the undeformed configuration at sufficiently large loads. Closed form analytic solutions are obtained for a specific material model, which may be viewed as a generalization of the classic neo-Hookean model to anisotropic materials. In contrast to the situation for a neo-Hookean sphere, bifurcation here may occur locally either to the right (supercritical) or to the left (subcritical), depending on the degree of anisotropy. In the latter case, the cavity has finite radius on first appearance. Such a discontinuous change in stable equilibrium configurations is reminiscent of the snap-through buckling phenomenon of structural mechanics. Such dramatic cavitational instabilities were previously encountered by Antman and Negr6n-Marrero [3] for anisotropic compressible solids and by Horgan and Pence 1-17] for composite incompressible spheres.

Abstract. The axial shear problem for a hollow circular cylinder, composed of homogeneous isotropic compressible nonlinearly elastic material, is described. The inner surf ice of the tube is bonded to a rigid cylinder while the outer surface is subjected to a uniformly distributed axial shear traction and the radial traction is zero. For an arbitrary compressible material, the cylinder will undergo both a radial and axial deformation. These axisymmetric fields are governed by a coupled pair of nonlinear ordinary differential equations, one of which is second-order and the other first-order. The class of materials for which axisymmetric anti-plane shear (i.e., a deformation with zero radial displacement) is possible is described. The corresponding axial displacement and stresses are determined explicitly. Specific material models are used to illustrate the results.