Tensile Fracture Loci for Brittle Materials Containing Spherical Voids

1986 ◽  
Vol 108 (3) ◽  
pp. 222-229 ◽  
Author(s):  
M. C. Shaw ◽  
J. P. Avery
Keyword(s):  
Three Dimensional ◽  
Brittle Materials ◽  
Dimensional Case ◽  
Tensile Fracture ◽  
Detailed Result ◽  
Three Dimension ◽  
Two Dimensional ◽  
Stress Criterion ◽  
Hydrostatic Tension ◽  
Spherical Voids

When very brittle materials are subjected to a complex state of stress they fail by maximum intensified tensile stress criterion first introduced by Griffith [1]. Nominal applied stresses are intensified by defects present in all real materials. It appears that defects controlling the strength of brittle materials are of two types—open ones characterized by circular voids found in sintered materials such as tungsten carbide and thin, essentially closed ones found in brittle polyphase rock such as granite. This paper is concerned with the extension of a very simple two dimensional theory for circular voids [3] to the three dimensional case involving spherical voids. While the fracture locus for the two dimensional case represents a conservative approximation sufficient for most engineering applications, the three dimension solution is necessary to give detailed result for cases involving near hydrostatic tension or compression.

Three-dimensional disturbances to a mixing layer in the nonlinear critical-layer regime

1995 ◽  
Vol 291 ◽  
pp. 57-81 ◽  
Author(s):  
S. M. Churilov ◽  
I. G. Shukhman
Keyword(s):  
Travelling Waves ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Critical Layer ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
New Type ◽  
Two Stages

We consider the nonlinear spatial evolution in the streamwise direction of slightly three-dimensional disturbances in the form of oblique travelling waves (with spanwise wavenumber kz much less than the streamwise one kx) in a mixing layer vx = u(y) at large Reynolds numbers. A study is made of the transition (with the growth of amplitude) to the regime of a nonlinear critical layer (CL) from regimes of a viscous CL and an unsteady CL, which we have investigated earlier (Churilov & Shukhman 1994). We have found a new type of transition to the nonlinear CL regime that has no analogy in the two-dimensional case, namely the transition from a stage of ‘explosive’ development. A nonlinear evolution equation is obtained which describes the development of disturbances in a regime of a quasi-steady nonlinear CL. We show that unlike the two-dimensional case there are two stages of disturbance growth after transition. In the first stage (immediately after transition) the amplitude A increases as x. Later, at the second stage, the ‘classical’ law A ∼ x2/3 is reached, which is usual for two-dimensional disturbances. It is demonstrated that with the growth of kz the region of three-dimensional behaviour is expanded, in particular the amplitude threshold of transition to the nonlinear CL regime from a stage of ‘explosive’ development rises and therefore in the ‘strongly three-dimensional’ limit kz = O(kx) such a transition cannot be realized in the framework of weakly nonlinear theory.

The Role of Three Dimension Computerized Imaging in Hand Surgery

1987 ◽  
Vol 12 (3) ◽  
pp. 349-352
Author(s):  
J. ENGEL ◽  
M. SALAI ◽  
B. YAFFE ◽  
R. TADMOR
Keyword(s):  
Three Dimensional ◽  
Hand Surgery ◽  
New Technique ◽  
Silicone Implants ◽  
Three Dimension ◽  
Two Dimensional ◽  
Radiological Imaging ◽  
Preliminary Results ◽  
Dimensional Picture

Three-dimensional computerized imaging is a new modality of radiological imaging. This new technique transforms the two-dimensional slices of bi-plane CT into a three-dimensional picture by a computer’s monitor adjusted to the system. This system enables the physician to rotate the angle of viewing of the desired region to any desired angle. Moreover, this system can delete certain features of different densities from the picture, such as silicone implants, thus improving visualization. Our preliminary results using this technique are presented. The advantages, pitfalls, and suggested future applications of this new technique in hand surgery are discussed.

On the Hydrodynamic Interaction Between Ship and Free-Surface Motions on Vessels With Moonpools

2019 ◽  
Author(s):  
Senthuran Ravinthrakumar ◽  
Trygve Kristiansen ◽  
Babak Ommani
Keyword(s):  
Free Surface ◽  
Flow Separation ◽  
Coupling Effect ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Navier Stokes ◽  
Linear Potential ◽  
Two Dimensional ◽  
Sloshing Mode ◽  
Vessel Motion

Abstract Coupling between moonpool resonance and vessel motion is investigated in two-dimensional and quasi three-dimensional settings, where the models are studied in forced heave and in freely floating conditions. The two-dimensional setups are with a recess, while the quasi three-dimensional setups are without recess. One configuration with recess is presented for the two-dimensional case, while three different moonpool sizes (without recess) are tested for the quasi three-dimensional setup. A large number of forcing periods, and three wave steepnesses are tested. Boundary Element Method (BEM) and Viscous BEM (VBEM) time-domain codes based on linear potential flow theory, and a Navier–Stokes solver with linear free-surface and body-boundary conditions, are implemented to investigate resonant motion of the free-surface and the model. Damping due to flow separation from the sharp corners of the moonpool inlets is shown to matter for both vessel motions and moonpool response around the piston mode. In general, the CFD simulations compare well with the experimental results. BEM over-predicts the response significantly at resonance. VBEM provides improved results compared to the BEM, but still over-predicts the response. In the two-dimensional study there are significant coupling effects between heave, pitch and moonpool responses. In the quasi three-dimensional tests, the coupling effect is reduced significantly as the moonpool dimensions relative to the displaced volume of the ship is reduced. The first sloshing mode is investigated in the two-dimensional case. The studies show that damping due to flow separation is dominant. The vessel motions are unaffected by the moonpool response around the first sloshing mode.

Pipe Response Under Concentrated Lateral Loads and External Pressure

2005 ◽  
Author(s):  
Spyros A. Karamanos ◽  
Charis Eleftheriadis
Keyword(s):  
Three Dimensional ◽  
External Pressure ◽  
Absorption Capacity ◽  
Pressure Effects ◽  
Analytical Models ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Lateral Loads ◽  
Offshore Pipelines ◽  
Different Levels

The present paper examines the denting deformation of offshore pipelines and tubular members (D/t≤50) subjected to lateral (transverse) quasi-static loading in the presence of uniform external pressure. Particular emphasis is given on pressure effects on the ultimate lateral load of tubes and on their energy absorption capacity. Pipe segments are modeled with shell finite elements, accounting for geometric and material nonlinearities, and give very good predictions compared with test data from non-pressurized pipes. Lateral loading between two rigid plates, a two-dimensional case, is examined first. Three-dimensional case, are also analyzed, where the load is applied either through a pair of opposite wedge-shaped denting tools or a single spherical denting tool. Load-deflection curves for different levels of external pressure are presented, which indicate that pressure has significant influence on pipe response and strength. Finally, simplified analytical models are proposed for the two-dimensional and three-dimensional load configurations, which yield closed-form expressions, compare fairly well with the finite element results and illustrate some important features of pipeline response in a clear and elegant manner.

The Role of Three-Dimension Computerized Imaging in Hand Surgery

1992 ◽  
Vol 17 (6) ◽  
pp. 702-702
Author(s):  
J. Engel ◽  
M. Salai ◽  
B. Yaffe ◽  
R. Tadmor
Keyword(s):  
Three Dimensional ◽  
Hand Surgery ◽  
New Technique ◽  
Silicone Implants ◽  
Three Dimension ◽  
Two Dimensional ◽  
Radiological Imaging ◽  
Preliminary Results ◽  
Dimensional Picture

Three-dimensional computerized imaging is a new modality of radiological imaging. This new technique transforms the two-dimensional slices of bi-plane CT into a three-dimensional picture by a computer's monitor adjusted to the system. This system enables the physician to rotate the angle of viewing of the desired region to any desired angle. Moreover, this system can delete certain features of different densities from the picture, such as silicone implants, thus improving visualization. Our preliminary results using this technique are presented. The advantages, pitfalls, and suggested future applications of this new technique in hand surgery are discussed.

Constitutive Inequalities for the Damage of Elastic-Brittle Materials

2011 ◽  
Vol 675-677 ◽  
pp. 891-899
Author(s):  
Qi Chang He ◽  
J.Z. Zhou
Keyword(s):  
Three Dimensional ◽  
Brittle Materials ◽  
Dimensional Case ◽  
Continuum Damage ◽  
One Dimensional ◽  
Damage Models ◽  
Constitutive Inequalities ◽  
The One

Starting from the requirement that the principle of determinism be satisfied, two constitutive inequalities are derived for one-dimensional strain- and stress-based continuum damage models. The one-dimensional constitutive inequality corresponding to the strain-based formulation turns out to be much less restrictive than the one associated to the stress-based formulation and is extended to the three-dimensional case. This extension gives a general constitutive inequality for the damage of elastic-brittle materials.

Void growth in shear

1986 ◽  
Vol 407 (1833) ◽  
pp. 435-458 ◽  
Keyword(s):  
Growth Rate ◽  
Strain Rate ◽  
Void Growth ◽  
Three Dimensional ◽  
Shape Evolution ◽  
Two Dimensional ◽  
Simple Shearing ◽  
Hydrostatic Tension ◽  
Dilatation Rate ◽  
Approximate Formulas

The growth of an isolated void is analysed for a void contained in a block of material undergoing simple shearing combined with superimposed hydrostatic tension. The evolution of the size, shape and orientation of two- and three-dimensional voids in an incompressible, linearly viscous solid is first discussed. The main problem addressed is the behaviour of a two-dimensional cylindrical void in an incompressible, nonlinearly viscous solid for which the strain rate varies as the stress to a power. The growth rate of the void and its shape evolution are strong functions of the degree of material nonlinearity. Relatively simple approximate formulas are obtained for the dilatation rate of a circular void as well as for the void potential. The constitutive relation of a block of material containing a dilute distribution of circular cylindrical voids is obtained directly using the isolated void potential. The paper concludes with a summary of available results for the dilatation rates of voids and cracks under combinations of shear and hydrostatic tension.

On: “Inversion of gravity profiles by use of a Backus‐Gilbert approach” by William R. Green (GEOPHYSICS, October 1975, p. 763–772).

Geophysics ◽  
1976 ◽  
Vol 41 (4) ◽  
pp. 777-777
Author(s):  
Ramesh Chander
Keyword(s):  
Gravity Anomaly ◽  
Total Mass ◽  
Gravity Data ◽  
Unit Length ◽  
Three Dimensional ◽  
Density Model ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Mass Excess ◽  
Seminal Paper

An important possible constraint on a density model obtained from inversion of gravity data has been overlooked in the seminal paper by Green. The computed density model should be such that the corresponding total mass excess or deficit per unit length in a two‐dimensional case, or total mass excess or deficit in a three‐dimensional case, should be comparable to the value obtained by applying Gauss’s theorem to the observed gravity anomaly data (Grant and West, 1965, p. 227–28 and p. 232).

Three-dimensional ray tracing and the method of principal curvature for geometric spreading

1983 ◽  
Vol 73 (3) ◽  
pp. 765-780
Author(s):  
Jia-Ju Lee ◽  
Charles A. Langston
Keyword(s):  
Principal Curvature ◽  
Three Dimensional ◽  
Seismic Energy ◽  
Front Surface ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Ray Method ◽  
P Waves ◽  
Curved Boundaries ◽  
Wave Source

abstract A three-dimensional ray method is used to compute three components of ground motion for complex structures involving curved boundaries. The method of principal curvature is developed to compute geometrical spreading of rays. This method, commonly used in electromagnetic wave propagation problems, employs phase matching at model interfaces and analysis of the wave front surface metric as the ray propagates throughout the model. It is an elegant way to examine the characteristics of three-dimensional caustics. Results computed for a two-dimensional canonical basin model with a plane SH-wave source are compared and are found to be in good agreement with those previously obtained by other independent numerical methods. Relaxing the restriction that the incident wave be perpendicular to the basin symmetry axis gives rise to large amplitude vertical and radial motions for incident SH waves and large tangential motions for incident P waves. As in the two-dimensional case, seismic energy is geometrically focused in the central region of the basin but strong later arrivals from the curved boundaries are not well developed in the three-dimensional case. The method is of direct use in analyzing three-dimensional crustal structure from off-azimuth P to S and S to P conversions.

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