The stress system generated by an electromagnetic field in a suspension of drops

The stress generated in a suspension of drops in the presence of a uniform electric field and a pure straining motion, taking into account that the magnetohydrodynamic effects are dominant was calculated. It was found that the stress generated in the suspension depended on the direction of the applied electric field, the dielectric constants, the vicosity coefficients, the conductivities, and the permeabilities of fluids inside and outside the drops. The expression of the particle stress shows that for fluids which are good conductors and poor dielectrics, especially for larger drops, magnetohydrodynamic effects end to reduce the dependence on the direction of the applied electric field

Regularity properties of the cubic nonlinear Schr\"odinger equation on the half line

In this paper we study the local and global regularity properties of the cubic nonlinear Schr\"odinger equation (NLS) on the half line with rough initial data. These properties include local and global wellposedness results, local and global smoothing results and the behavior of higher order Sobolev norms of the solutions. In particular, we prove that the nonlinear part of the cubic NLS on the half line is smoother than the initial data. The gain in regularity coincides with the gain that was observed for the periodic cubic NLS \cite{et2} and the cubic NLS on the line \cite{erin}. We also prove that in the defocusing case the norm of the solution grows at most polynomially-in-time while in the focusing case it grows exponentially-in-time. As a byproduct of our analysis we provide a different proof of an almost sharp local wellposedness in $H^s(\R^+)$. Sharp $L^2$ local wellposedness was obtained in \cite{holmer} and \cite{bonaetal}. Our methods simplify some ideas in the wellposedness theory of initial and boundary value problems that were developed in \cite{collianderkenig, holmer,holmer1,bonaetal}.Comment: 30 pages. Minor revisions. To appear in Journal of Functional Analysi

The Crack-contact and the Free End Problem for a Strip Under Residual Stress

The plane problem for an infinite strip with two edge cracks under a given state of residual stress is considered. The residual stress is compressive near and at the surfaces and tensile in the interior of the strip. If the crack is deep enough to penetrate into the tensile zone, then the problem is one of crack-contact problem in which the depth of the contact area is an unknown which depends on the crack depth and the residual stress profile. The problem has applications to the static fatigue of glass plates and is solved for three typical residual stress profiles. In the limiting case of the crack crossing the entire plate thickness, the problem becomes a stress-free end problem for a semi-infinite strip under a given residual stress state away from the end. This is a typical stress diffusion problem in which decay behavior of the residual stress near and the nature of the normal displacement at the end of the semi-infinite strip are of special interest. For two typical residual stress states the solution is obtained, and some numerical results are given

The use of COD and plastic instability in crack propagation and arrest in shells

The initiation, growth, and possible arrest of fracture in cylindrical shells containing initial defects are dealt with. For those defects which may be approximated by a part-through semi-elliptic surface crack which is sufficiently shallow so that part of the net ligament in the plane of the crack is still elastic, the existing flat plate solution is modified to take into account the shell curvature effect as well as the effect of the thickness and the small scale plastic deformations. The problem of large defects is then considered under the assumptions that the defect may be approximated by a relatively deep meridional part-through surface crack and the net ligament through the shell wall is fully yielded. The results given are based on an 8th order bending theory of shallow shells using a conventional plastic strip model to account for the plastic deformations around the crack border

Crack opening stretch in a plate of finite width

The problem of a uniaxially stressed plate of finite width containing a centrally located damage zone is considered. It is assumed that the flaw may be represented by a part-through crack perpendicular to the plate surface, the net ligaments in the plane of the crack and through-the-thickness narrow strips ahead of the crack ends are fully yielded, and in the yielded sections the material may carry only a constant normal traction with magnitude equal to the yield strength. The problem is solved by neglecting the bending effects and the crack opening stretches at the center and the ends of the crack are obtained. Some applications of the results are indicated by using the concepts of critical crack opening stretch and constant slope plastic instability

Fracture of composite panels

The fracture problem in panels consisting of periodically arranged load carrying and buffer strips of different materials is considered. The main emphasis is placed on the problem of a crack terminating at and crossing the interfaces and on the stress free end problem. The problem is formulated in terms of a system of singular integral equations, and numerical solutions are obtained for certain material combinations. With the study of possible crack propagation and delamination in mind, certain stress intensity factors are defined and calculated. A main result is that when the crack touches or intersects a bimaterial interface, the stress state has no longer the standard square root singularity, and, to study further propagation of the crack, the conventional fracture models need to be modified, or new models need to be developed