Elastic Continuum Approach Research Articles

Winkler Coefficient for Beams on Elastic Foundation

Using the elastic continuum approach for the analysis ofbeam on elastic foundation, a method is developed to calculate an equivalent coefficient of subgrade reaction k to use in the Winkler model. It is shown that dividing the contact pressure produced from elastic continuum model by the corresponding settlement along the beam length generates length dependent coefficient of subgrade reaction that accurately describes the interaction between the beam and the supporting soils. Results from the developed I equivalent k parameter are compared with those from elastic continuum model and by using different k values predicted by other methods that are currently in use. For uniformly loaded beam, graphs and regression equations are provided from which an equivalent k value at different positions along the beam length (eg, at the center and the edge of the beam) can be calculated as a function of the elastic soil properties and the rigidity of the beam

Evolution of gas-filled nanocracks in crystalline solids.

In this work, the evolution of gas-filled cracks under gas implantation and subsequent annealing is studied on the basis of an elastic continuum approach. The observed growth limitation of He-filled nanocracks in SiC is attributed to their stabilization by the formation of circular dislocation dipoles. The formation and Ostwald ripening of bubble-loop complexes at elevated temperatures is modeled in terms of gas atom exchange between such complexes coupled with local matrix atom exchange between bubbles and loops of the same complex. The scaling laws derived for the time dependence of bubble and loop sizes are found to be in good agreement with experimental data.

Metal/ceramic interfaces: a microscopic analysis

AbstractThis contribution treats the fundamental and practical aspects of the analysis of interfaces between metals and ceramic materials. It is shown that, in principle at least, it is possible to assess the bond strength by investigating the atomic structure of the dislocation cores. We have chosen to exemplify our approach with the misfit‐dislocation structures at two, crystallographically different, systems, i.e. cube‐on‐cube and cube‐on‐non cube interfaces. It turns out that from high‐resolution transmission electron microscopy observations in combination with computer modelling studies a qualitative insight can be obtained about the bonding behaviour between these dissimilar materials. In general we may conclude that there is a fair correlation between the atomistic and linear elastic continuum description of interface dislocations. However, it is shown that the linear elastic continuum approach cannot account for the possible configurations at an interface with misfit, because it does not include the effects of different bonding strengths on the interface structure. This contribution directs also to some future experimental work. Segregation of other elements might affect the local bond strength which may become manifest in the experimental observations of atomic structure. Copyright © 2001 John Wiley & Sons, Ltd.

Flexural Analysis of Prestressed Concrete Sandwich Panels with Truss Connectors

A closed form elastic continuum approach was modified to account for discrete truss connectors to estimate service load deflections and bending stresses of non-loadbearing semi-composite sandwich panels. Predictions of maximum deflections and bending stresses were compared to finite element results and experimental data. Close agreement was found between the two analytical approaches, and both methods produced conservative predictions as compared to experimental data. Sensitivity analyses indicate the presence of unidentified additional shear transfer mechanisms in actual panels that are not fully represented in the elastic models. However, the theory holds promise for design and for understanding the behavior of semi-composite sandwich panels.

Misfit dislocations: An atomistic and elastic continuum approach

This paper presents the results of an atomistic model in which the misfit and the bond strength between a metal and a substrate can be controlled. The model is applied to a simple case, i.e. an interface with misfit in one direction. Calculated energies are presented and the corresponding atomic structures for various misfits and interaction parameters are discussed. It turned out that the structure of the misfit dislocations depends both on misfit and bond strength. A trend from delocalized structures to localized structures that resemble bulk-like dislocations can be seen for decreasing misfit at constant interaction parameter, and increasing interaction parameter at constant misfit. This atomistic approach is compared with a description based on linear elasticity theory of interface dislocations. Although a fair correlation exists between these two different concepts, it is shown that the elastic continuum approach cannot account for the possible configurations at an interface, because it does not contain any information on the effects different bond strengths may have on the interface structure.

Energetics and formation kinetics of helium bubbles in metals

Abstract Recent theoretical work on the energetics and formation kinetics of helium bubbles in metals is reviewed. The energetics are discussed in particular for bubbles with radii between 10 and 1000 Å containing helium under very high pressures (nonideal gas bubbles). For this size range, the bubble formation free energy is split into three parts: a helium bulk free energy which is considered for solid and fluid helium (high-density equation of state), a bubble-matrix interface free energy for which curvature corrections are introduced, and a relaxation energy which is treated within the elastic continuum approach. The formation kinetics are considered for two extreme cases. For high helium production rates and low temperatures, helium clustering is associated with athermal processes such as metal interstitial emission and dislocation loop punching. For dislocation loop punching, an interpolation between computer simulation and continuum-theory results is discussed. For low helium production rates and high temperatures, helium clustering is connected with vacancy absorption. For this case, nucleation kinetics are briefly sketched while growth kinetics are analyzed in some detail with special reference to the effects of the high helium densities in the bubbles. In particular, the transition from gas-driven to vacancy supersaturation-driven bubble growth and its role for the evolution of bimodal bubble size distributions are analyzed. Reliable criteria to to discriminate between the two main bubble-coarsening mechanisms, bubble coalescence and Ostwald ripening, are suggested. The procedure to derive the activation energy of gas permeation from bubble coarsening, identified as Ostwald ripening is discussed.

Surface acoustic wave propagation in MnF2

The temperature and magnetic field dependence of surface acoustic wave velocities in MnF2 single crystals has been investigated. Wave propagation was on a free (001)-plane in [100] and [110]-direction. The temperature dependence can be explained quantitatively by an elastic continuum approach. Experiments reveal the bulk spin flop at Bc∼9.3 T at 4.2 K. No evidence is found for a surface spin flop at lower field, Bsc∼6.6 T.

Theoretical t - z Curves

Most procedures to compute the t-z (stress-displacement) response for axial pile loading are empirical, based mostly on data for pile diameters less than 18 in. (0.15 m) and pile penetrations less than 100 ft (30 m). These procedures may not be appropriate for pile and soil conditions that differ from those on which the procedures were developed. Therefore, a theoretical procedure is developed to generate t-z curves for predicting pile movements under axial load. The procedure uses an approximate one-dimensional, elastic continuum approach to define the t-z response up to the maximum t response and laboratory simulation to define the post-peak response. The procedure was used with several case studies. Predicted response of the pile under axial loading was in good agreement with the measured response.