Configurational Forces on Elastic Line Singularities

2018 ◽  
Vol 85 (3) ◽  
Author(s):  
Youjung Seo ◽  
Gyu-Jin Jung ◽  
In-Ho Kim ◽  
Y. Eugene Pak
Keyword(s):  
Edge Dislocation ◽  
Strain Energy ◽  
Configurational Forces ◽  
Elastic Line ◽  
Line Force ◽  
Self Similar ◽  
Expansion Force ◽  
Line Singularities ◽  
Concentrated Couple ◽  
M Integral

Configurational forces acting on two-dimensional (2D) elastic line singularities are evaluated by path-independent J-, M-, and L-integrals in the framework of plane strain linear elasticity. The elastic line singularities considered in this study are the edge dislocation, the line force, the nuclei of strain, and the concentrated couple moment that are subjected to far-field loads. The interaction forces between two similar parallel elastic singularities are also calculated. Self-similar expansion force, M, evaluated for the line force shows that it is exactly the negative of the strain energy prelogarithmic factor as in the case for the well-known edge dislocation result. It is also shown that the M-integral result for the nuclei of strain and the L-integral result for the line force yield interesting nonzero expressions under certain circumstances.

A Green’s Function Formulation of Anticracks and Their Interaction With Load-Induced Singularities

1989 ◽  
Vol 56 (3) ◽  
pp. 550-555 ◽  
Author(s):  
John Dundurs ◽  
Xanthippi Markenscoff
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Edge Dislocation ◽  
Weight Functions ◽  
Bimaterial Interface ◽  
Elastic Fields ◽  
Function Formulation ◽  
Concentrated Forces ◽  
Concentrated Couple ◽  
Working Out

This paper provides a Green’s function formulation of anticracks (rigid lamellar inclusions of negligible thickness that are bonded to the surrounding elastic material). Apart from systematizing several previously known solutions, the article gives the pertinent fields for concentrated forces, dislocations, and a concentrated couple applied on the line of the anticrack. There is a reason for working out these results: In contrast to concentrated forces, a concentrated couple approaching the tip of an anticrack makes the elastic fields explode. Finite limits can be achieved, however, by appropriately diminishing the magnitude of the couple, which then leads to fields that are intimately connected with the weight functions for the anticrack. An edge dislocation going to the tip of an anticrack puts a net force on the lamellar inclusion, which is shown to be related to a previously known feature of dislocations near a bimaterial interface.

Higher Order Singularities and Their Energetics in Elastic-Plastic Fracture

2000 ◽  
Author(s):  
Seyoung Im ◽  
Insu Jeon
Keyword(s):  
Conservation Laws ◽  
Interaction Energy ◽  
Higher Order ◽  
Configurational Forces ◽  
J Integral ◽  
Numerical Examples ◽  
Elastic Plastic ◽  
M Integral

Abstract The higher order singularities[1] are systematically examined, and discussed are their complementarity relation with the nonsingular eigenfunctions and their relations to the configurational forces like J-integral and M-integral. By use of the so-called two state conservation laws[2] or interaction energy, originally proposed by Eshelby[3] and later treated by Chen and Shield[4], the intensities of the higher order singularities are calculated, and their roles in elastic-plastic fracture are investigated. Numerical examples are presented for illustration.

scholarly journals Magnetohydrodynamic Winds Driven by Line Force from the Standard Thin Disk around Supermassive Black Holes: II. A Possible Model for Ultra-fast Outflows in Radio-loud AGNs

2021 ◽  
Vol 922 (2) ◽  
pp. 262
Author(s):  
Xiao-Hong Yang
Keyword(s):  
Magnetic Field ◽  
Numerical Simulations ◽  
Inclination Angle ◽  
Initial Conditions ◽  
Disk Surface ◽  
Similar Solution ◽  
Driving Mechanism ◽  
Self Similar Solution ◽  
Line Force ◽  
Self Similar

Abstract In radio-loud active galactic nuclei (AGNs), ultra-fast outflows (UFOs) were detected at the inclination angle of ∼10°–70° away from jets. Except for the inclination angle of UFOs, the UFOs in radio-loud AGNs have similar properties to that in radio-quiet AGNs. The UFOs with such low inclination cannot be explained in the line-force mechanism. The magnetic-driving mechanism is suggested to explain the UFOs based on a self-similar solution with radiative transfer calculations. However, the energetics of self-similar solution need to be further confirmed based on numerical simulations. To understand the formation and acceleration of UFOs in radio-loud AGNs, this paper presents a model of the disk winds driven by both line force and magnetic field and implements numerical simulations. Initially, a magnetic field is set to 10 times stronger than the gas pressures at the disk surface. Simulation results imply that the disk winds driven by both line force and magnetic field could describe the properties of UFOs in radio-loud AGNs. Pure magnetohydrodynamics (MHDs) simulation is also implemented. When the initial conditions are the same, the hybrid models of magnetic fields and line force are more helpful to form UFOs than the pure MHD models. It is worth studying the case of a stronger magnetic field to confirm this result.

scholarly journals Riemannian surfaces with torsion as homogenization limits of locally Euclidean surfaces with dislocation-type singularities

2016 ◽  
Vol 146 (4) ◽  
pp. 741-768 ◽  
Author(s):  
Raz Kupferman ◽  
Cy Maor
Keyword(s):  
Edge Dislocation ◽  
Smooth Manifolds ◽  
Affine Connections ◽  
Riemannian Surfaces ◽  
Dislocation Type ◽  
Classical Models ◽  
The 1950S ◽  
Weak Notion ◽  
Line Singularities ◽  
Edge Dislocations

We reconcile two classical models of edge dislocations in solids. The first, from the early 1900s, models isolated edge dislocations as line singularities in locally Euclidean manifolds. The second, from the 1950s, models continuously distributed edge dislocations as smooth manifolds endowed with non-symmetric affine connections (equivalently, endowed with torsion fields). In both models, the solid is modelled as a Weitzenböck manifold. We prove, using a weak notion of convergence, that the second model can be obtained rigorously as a homogenization limit of the first model as the density of singular edge dislocation tends to infinity.

Two Dynamic Fracture Problems Concerning Bridging Fiber Pull-Out of Composite Materials

2010 ◽  
Vol 177 ◽  
pp. 173-177
Author(s):  
Nian Chun Lü ◽  
Yun Hong Cheng ◽  
Yun Tao Wang
Keyword(s):  
Composite Materials ◽  
Dynamic Fracture ◽  
Strain Energy ◽  
Hilbert Problem ◽  
Strain Energy Release ◽  
Dynamic Stress Intensity Factors ◽  
Pull Out ◽  
Complex Functions ◽  
Self Similar ◽  
Superposition Theorem

By means of the built dynamic fracture model of bridging fiber pull-out of composite materials, the problems considered will be transformed into Riemann-Hilbert problem in terms of the theory of complex functions. Analytical solutions of the stresses displacements, dynamic stress intensity factors, strain energy release rate and bridging fibrous fracture speeds under the conditions of an moving increasing loads, Pt/x, Px2/t, respectively, can be facilely obtained by the approaches of self-similar functions. After those solutions were utilized by superposition theorem, the solutions of arbitrary complex problems can be attained.

Mode III Interfacial Edge Crack in a Magnetoelectroelastic Bimaterial

2004 ◽  
Vol 261-263 ◽  
pp. 393-398 ◽  
Author(s):  
Ai Kah Soh ◽  
Jin Xi Liu
Keyword(s):  
Edge Crack ◽  
Electric Displacement ◽  
Mapping Technique ◽  
Mode Iii ◽  
Variable Approach ◽  
Out Of Plane ◽  
Line Force ◽  
Closed Form Analytical Solution ◽  
Line Singularities ◽  
Magnetoelectroelastic Bimaterial

This paper deals with a Mode III interfacial edge crack in a magnetoelectroelastic bimaterial subjected to line singularities such as an out-of-plane line force, a line electric charge, a line magnetic charge and a straight screw dislocation. The surfaces (including crack surfaces) of the bimateral are assumed to be electrically open and magnetically closed. The closed-form analytical solution to the problem is obtained by employing the complex variable approach in conjunction with the conformal mapping technique. The intensity factors of stress, electric displacement and magnetic induction are given explicitly. The obtained results can be used as the Green's function to solve more complicated problems.

Antiplane Eigenstrain Problem of an Elliptic Inclusion in a Two-Phase Anisotropic Medium

1985 ◽  
Vol 52 (1) ◽  
pp. 87-90 ◽  
Author(s):  
H. T. Zhang ◽  
Y. T. Chou
Keyword(s):  
Anisotropic Medium ◽  
Strain Energy ◽  
Homogeneous Medium ◽  
Stress Singularity ◽  
Elliptic Inclusion ◽  
Two Phase ◽  
Line Force ◽  
Elastic Inhomogeneity ◽  
Inhomogeneity Factor ◽  
Force Concept

An antiplane eigenstrain problem of an elliptic inclusion in a two-phase anisotropic medium is analyzed based on the line-force concept. Explicit expressions for the stress field and strain energy are obtained under a given symmetry. The results are used to determine the stress singularity coefficient for a flat inclusion. When the tip of the inclusion is located at the interface boundary, the stress singularity coefficient S′ varies according to the formula S′ = (1 + K) S° where K is the elastic inhomogeneity factor and S° is the stress singularity coefficient for a homogeneous medium (K = 0).

The wustite-spinel interface

1987 ◽  
Vol 45 ◽  
pp. 268-269
Author(s):  
S.R. Summerfelt ◽  
C.B. Carter
Keyword(s):  
Solid State ◽  
Solid State Reaction ◽  
Strain Energy ◽  
Matrix Material ◽  
Lattice Misfit ◽  
Solid State Reactions ◽  
Oxygen Sublattice ◽  
Large Particles ◽  
Small Lattice ◽  
Coherent Interfaces

The wustite-spinel interface can be viewed as a model interface because the wustite and spinel can share a common f.c.c. oxygen sublattice such that only the cations distribution changes on crossing the interface. In this study, the interface has been formed by a solid state reaction involving either external or internal oxidation. In systems with very small lattice misfit, very large particles (>lμm) with coherent interfaces have been observed. Previously, the wustite-spinel interface had been observed to facet on {111} planes for MgFe2C4 and along {100} planes for MgAl2C4 and MgCr2O4, the spinel then grows preferentially in the <001> direction. Reasons for these experimental observations have been discussed by Henriksen and Kingery by considering the strain energy. The point-defect chemistry of such solid state reactions has been examined by Schmalzried. Although MgO has been the principal matrix material examined, others such as NiO have also been studied.

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