Predictions Of Elasticity Theory Research Articles

Buckling of thin plates in the weakly and strongly nonlinear regimes

Abstract The buckling of thin plates is interesting from the point of view of materials science, because it provides a rather unique opportunity of exploring the predictions of elasticity theory in non-trivial conditions and allows in a specific example to disentangle new physical effects from effects that can be explained in the framework of the fundamental equations. I review these basic Föppl-von Karman equations for the elasticity of thin plates and then study the two limits of weak and strong nonlinear regimes for buckling.

Buckling of thin plates in the weakly and strongly nonlinear regimes

Abstract The buckling of thin plates is interesting from the point of view of materials science, because it provides a rather unique opportunity of exploring the predictions of elasticity theory in non-trivial conditions and allows in a specific example to disentangle new physical effects from effects that can be explained in the framework of the fundamental equations. I review these basic Föppl-von Karman equations for the elasticity of thin plates and then study the two limits of weak and strong nonlinear regimes for buckling.

Cluster/dislocation interactions in dilute aluminum-based solid solutions

The influence of single solute atoms and solute clusters on an extended edge dislocation dipole in Al was studied by atomistic simulation. Single Cu and Ag solute/dislocation interaction energy calculations showed that Cu interacts strongly with an Al extended dislocation and prefers sites in the compressive region, in agreement with elasticity theory predictions. Single Ag atoms, however, are strongly repelled by an Al extended dislocation, in contrast with elasticity theory predictions. Monte Carlo simulations of Al: 1% Cu, Al: 2% Cu, Al: 1% Ag, Al: 0.5% Cu, 0.5% Ag, and Al: 0.75% Cu, 0.25% Ag were carried out in the presence of an extended dislocation dipole at 600 K allowing for solute segregation. Cu atoms in the binary alloys were observed to segregate to the compressive regions of the extended dislocation dipole, forming widespread “atmospheres” over the width of both extended dislocations which did not affect the partial dislocation spacing. Ag in the binary alloy formed small Ag zones which also had little influence on the spacing between the partials. The ternary systems, however, exhibited highly localized solute clusters that had a large impact on the extended dislocation dipole structure, increasing the separation between the partial dislocations. The resulting cluster structures are discussed along with their influence on the apparent stacking fault energy of the alloy systems.

The effect of intrinsic curvature on supercoiling: predictions of elasticity theory.

Elasticity theory of naturally curved rods is employed to study the effects of intrinsic curvature on the properties of the equilibrium conformations of supercoiled DNA. The results stand in sharp contrast to those obtained when the molecule is viewed as being straight in its relaxed form. Starting from very fundamental principles of the theory, we show that the torsion of an open segment with a curved duplex axis can vary when the temperature, and along with it, the intrinsic twist is changed. Conversely, an imposed helicity, such as might be associated with binding to a histone, can change the intrinsic twist. It is also shown that another consequence of the presence of naturally curved sequences is that the twist density will, in general, vary with position along the chain in all equilibrium states. Then portions of the molecule will be more or less susceptible to interaction with other agents sensitive to such a variation. Finally, some closed equilibrium global structures uniquely associated with intrinsic curvature are discussed.

Breakdown of continuum elasticity theory in the limit of monatomic films.

We demonstrate that the predictions of continuum elasticity theory fail in the ultimate limit of monolayer films. We directly measure the lattice distortion of ultrathin InAs layers in GaAs by high-resolution electron microscopy. For InAs films of 3 monolayer thickness, the observed tetragonal distortion agrees with the prediction of elasticity theory. For single InAs monolayers, however, the measured strain is much higher than expected. The InAs unit cell in this case is strained such as to conserve the bulk bond length at the interface.

Pointwise errors in the classical and in Reissner's linear theory of plates, especially for concentrated loads

An infinite, horizontal, elastically isotropic plate is subjected to a distributed vertical, axisymmetric load, part of which is a body force and part of which is a surface traction. The resulting 3-dimensional stresses and displacements are found with the aid of Love's stress function and Hankel transforms. From these, the sum of the principal stress couples, the average rotation of radial fibers, and the average vertical deflection are computed and compared against the predictions of classical and Reissner's shear-deformation plate theory. Remarkably, the elasticity and plate theory predictions for the stress couples and the rotation agree if Poisson's ratio is zero. In general, for smoothly varying loads, the predictions of Reissner's theory are closer than those of classical theory to the predictions of elasticity theory. However, if a part of the load is (nearly) concentrated, then it is shown that the singularities in the sum of the principal stress couples and in the rotation predicted by Reissner's theory are too strong (because his theory accounts for normal stress effects based on smoothly varying loads). Moreover, if the concentrated part of the external load is a uniformly distributed line load through the thickness, then classical theory predicts the correct singularity in these variables, although with an erroneous strength. On the other hand, Reissner's theory correctly predicts the logarithmic singularity in the average vertical deflection (for any type of concentrated load), although with an erroneous strength.

Measurement of infrared absorptivities and line shapes and the distortion of anvils in diamond-anvil cells

The infrared transmission of diamond and other transparent anvil apparatuses that contain absorbing samples, has been calculated as a function of frequency for planar anvils that are inclined to one another or that are distorted into parabolic shapes. At frequencies where the samples are completely transparent, the height of the interference fringes decreases with increase of frequency at nearly the same rate for both parabolically distorted and inclined anvils for which the maximum difference in optical path length of the sample is the same. Hence, the distortion of anvils in a typical experimental configuration have been measured up to a mean pressure on the anvil faces of 60 kbar. They are consistent with the predictions of elasticity theory that distortions occur at the rate of about 20 μm in 500 kbar. The predicted effect of such distortions on the absorbance, integrated area, and time autocorrelation function of the dipole moment is insignificant in a well-designed experiment, and so all these properties can now be measured accurately at high pressures.

Surface Energy for Brittle Fracture in Metals from Phonon Frequencies

A new method is presented for calculating the surface energy for brittle fracture in a solid. Use is made of the knowledge of some features of the crystal dynamics as well as of the Debye, melting, and boiling temperatures of the material. Predicted values for the surface energy of a number of metals are compared with those based on the elastic theory and with the experimental ones. In particular, easy cleavage of zinc and, in contrast with recent predictions of elastic theory, the preferred plane of fracture in tungsten and beryllium are made plausible.

Reinforced concrete under thermal gradients

Summary The significance and current knowledge of thermal effects in concrete and reinforced concrete are reviewed briefly. It is evident that there is a need for more basic data on the shrinkage and creep of concrete subjected to high temperatures. Tests designed to obtain some of these data are described; results for the shrinkage and creep of a particular concrete at temperatures up to l40°C are presented. Some of the specimens were sealed to prevent loss of moisture, to simulate the conditions in mass concrete. It is shown that the time-dependent strains are markedly temperature-dependent. The paper then describes tests on model reinforced concrete beams subjected to a thermal gradient while flexurally restrained but without longitudinal restraint. The behaviour of the unsealed beams showed a severe departure from the predictions of conventional elastic theory, even to the extent of indicating compression in the reinforcing steel, instead of the expected tension. This was due to shrinkage and creep under the high temperatures. The behaviour of the sealed reinforced concrete specimens approximated to the predictions of elastic theory with a low value of the elastic modulus. A numerical procedure for estimating approximately the effects of time- and temperature-dependent strains in flexurally restrained beams is outlined in an Appendix.