Sliding Inclusions and Inhomogeneities With Frictional Interfaces

1992 ◽  
Vol 59 (4) ◽  
pp. 783-788 ◽  
Author(s):  
R. Furuhashi ◽  
Jin H. Huang ◽  
T. Mura
Keyword(s):  
Exact Solution ◽  
Shear Stress ◽  
Closed Form ◽  
Spherical Inclusion ◽  
Existence Of Solution ◽  
Elastic Fields ◽  
Uniform Shear ◽  
Ellipsoidal Inhomogeneity ◽  
Applied Shear Stress ◽  
Frictional Interface

Elastic fields due to a sliding inclusion and inhomogeneity with the frictional interface are investigated. The exact solution in closed form is presented for three cases: (i) a spherical inclusion which undergoes constant eigenstrains, (ii) a nondegenerate ellipsoidal inclusion with uniform shear eigenstrains and (iii) a nondegenerate ellipsoidal inhomogeneity subjected to an applied shear stress at infinity. Moreover, the existence of solution for a sliding inclusion and inhomogeneity with frictional interface is also demonstrated.

A Spherical Inclusion in an Elastic Half-Space Under Shear

1997 ◽  
Vol 64 (3) ◽  
pp. 471-479 ◽  
Author(s):  
I. Jasiuk ◽  
P. Y. Sheng ◽  
E. Tsuchida
Keyword(s):  
Half Space ◽  
Spherical Inclusion ◽  
Transformation Strain ◽  
Elastic Half Space ◽  
Elastic Fields ◽  
Surrounding Matrix ◽  
Uniform Shear ◽  
The Matrix ◽  
Displacement Potentials ◽  
Space Matrix

We find the elastic fields in a half-space (matrix) having a spherical inclusion and subjected to either a remote shear stress parallel to its traction-free boundary or to a uniform shear transformation strain (eigenstrain) in the inclusion. The inclusion has distinct properties from those of the matrix, and the interface between the inclusion and the surrounding matrix is either perfectly bonded or is allowed to slip without friction. We obtain an analytical solution to this problem using displacement potentials in the forms of infinite integrals and infinite series. We include numerical examples which give the local elastic fields due to the inclusion and the traction-free surface.

Elastic Fields in a Polygon-Shaped Inclusion With Uniform Eigenstrains

1997 ◽  
Vol 64 (3) ◽  
pp. 495-502 ◽  
Author(s):  
H. Nozaki ◽  
M. Taya
Keyword(s):  
Composite Materials ◽  
Closed Form ◽  
Strain Field ◽  
Strain Energy ◽  
Convex Polygon ◽  
Numerical Examples ◽  
Elastic Fields ◽  
Closed Form Solutions ◽  
Arbitrary Convex ◽  
Shaped Inclusion

In this paper the elastic fields in an arbitrary, convex polygon-shaped inclusion with uniform eigenstrains are investigated under the condition of plane strain. Closed-form solutions are obtained for the elastic fields in a polygon-shaped inclusion. The applications to the evaluation of the effective elastic properties of composite materials with polygon-shaped reinforcements are also investigated for both dilute and dense systems. Numerical examples are presented for the strain field, strain energy, and stiffness of the composites with polygon shaped fibers. The results are also compared with some existing solutions.

Propagation of a Sudden Rotary Disturbance in an Elastic Plate in Plane Stress

1956 ◽  
Vol 23 (2) ◽  
pp. 284-286
Author(s):  
J. N. Goodier ◽  
W. E. Jahsman
Keyword(s):  
Shear Stress ◽  
Radial Velocity ◽  
Plane Stress ◽  
Elastic Plate ◽  
Uniform Shear ◽  
Subsequent Motion

Abstract Detailed results are found for two plane-stress problems of an elastic plate with a hole from which a symmetrical disturbance is propagated. In the first a uniform shear stress is suddenly applied and maintained at the hole. In the second a uniform (rotary) velocity is suddenly applied and maintained. The subsequent motion is entirely rotary and involves shear stress only. The problems are mathematically analogous to those of symmetrical pressure and radial velocity at the hole, already solved by Kromm, and his analysis is followed. The existence of a similar analogy in the statical cases is well known.

scholarly journals Inversion of higher order isotropic tensors with minor symmetries and solution of higher order heterogeneity problems

2010 ◽  
Vol 467 (2126) ◽  
pp. 314-332 ◽  
Author(s):  
Vincent Monchiet ◽  
Guy Bonnet
Keyword(s):  
Closed Form ◽  
Strain Field ◽  
Spherical Inclusion ◽  
Higher Order ◽  
Quadratic Polynomial ◽  
Elastic Matrix ◽  
Closed Form Expression ◽  
Form Expression ◽  
Order Tensor ◽  
Strain Fields

In this paper, the derivation of irreducible bases for a class of isotropic 2 n th-order tensors having particular ‘minor symmetries’ is presented. The methodology used for obtaining these bases consists of extending the concept of deviatoric and spherical parts, commonly used for second-order tensors, to the case of an n th-order tensor. It is shown that these bases are useful for effecting the classical tensorial operations and especially the inversion of a 2 n th-order tensor. Finally, the formalism introduced in this study is applied for obtaining the closed-form expression of the strain field within a spherical inclusion embedded in an infinite elastic matrix and subjected to linear or quadratic polynomial remote strain fields.

scholarly journals Exaggerated cation leak from oxygenated sickle red blood cells during deformation: evidence for a unique leak pathway

Blood ◽  
1992 ◽  
Vol 80 (9) ◽  
pp. 2374-2378
Author(s):  
T Sugihara ◽  
RP Hebbel
Keyword(s):  
Shear Stress ◽  
Lipid Hydroperoxide ◽  
Viscous Medium ◽  
Permeability Barrier ◽  
Biochemical Basis ◽  
Rbc Membrane ◽  
Gardos Channel ◽  
Ambient Oxygen ◽  
Applied Shear Stress ◽  
Leak Pathway

An abnormal susceptibility of the sickle red blood cell (RBC) membrane to deformation could compromise its permeability barrier function and contribute to the exuberant cation leakiness occurring during the sickling phenomenon. We examined this hypothesis by subjecting RBCs at ambient oxygen tension to elliptical deformation, applying shear stress in a viscous medium under physiologic conditions. Compared with normal and high-reticulocyte control RBCs, sickle RBCs manifest an exaggerated K leak response to deformation. This leak is fully reversible, is both Cl and Ca independent, and at pHe 7.4 is fully balanced so that Kefflux equals Nainflux. This abnormal susceptibility is also evident in that the K leak in response to deformation occurs at an applied shear stress of only 141 dyne/cm2 for sickle RBCs, as compared to 204 dyne/cm2 for normal RBCs. Fresh sickle RBC membranes contain elevated amounts of lipid hydroperoxide, the presence of which is believed to provide the biochemical basis for enhanced deformation susceptibility. When examined at pHe 6.8, oxygenated sickle RBCs acquire an additional, unbalanced (Kefflux > Nainflux) component to the K leak increment specifically ascribable to deformation. Studies with inhibitors suggest that this additional component is not caused by a known leak pathway (eg, either K:Cl cotransport or the Gardos channel). This abnormal susceptibility of the sickle membrane to development of cation leakiness during deformation probably contributes to the exuberant cation leak taking place during RBC sickling.

The Elastic Field of an Elliptic Inclusion With a Slipping Interface

1986 ◽  
Vol 53 (1) ◽  
pp. 103-107 ◽  
Author(s):  
E. Tsuchida ◽  
T. Mura ◽  
J. Dundurs
Keyword(s):  
Closed Form ◽  
Infinite Series ◽  
Elastic Field ◽  
Elliptic Inclusion ◽  
Numerical Examples ◽  
Elastic Fields ◽  
Bonded Interface ◽  
The Matrix ◽  
Displacement Potentials ◽  
Uniform Expansion

The paper analyzes the elastic fields caused by an elliptic inclusion which undergoes a uniform expansion. The interface between the inclusion and the matrix cannot sustain shear tractions and is free to slip. Papkovich–Neuber displacement potentials are used to solve the problem. In contrast to the perfectly bonded interface, the solution cannot be expressed in closed form and involves infinite series. The results are illustrated by numerical examples.

On the Dynamic Growth of a Spherical Inclusion With Dilatational Transformation Strain in Infinite Elastic Domain

1999 ◽  
Vol 66 (4) ◽  
pp. 879-884 ◽  
Author(s):  
B. Wang ◽  
Q. Sun ◽  
Z. Xiao
Keyword(s):  
Hydrostatic Stress ◽  
Spherical Inclusion ◽  
Reduction Rate ◽  
Dynamic Effect ◽  
Propagation Speed ◽  
Transformation Strain ◽  
Elastic Fields ◽  
Initiation And Propagation ◽  
Dynamic Growth ◽  
Basic Ideas

In this paper, the dynamic effect was incorporated into the initiation and propagation process of a transformation inclusion. Based on the time-varying propagation equation of a spherical transformation inclusion with pure dilatational eigenstrain, the dynamic elastic fields both inside and outside the inclusion were derived explicitly, and it is found that when the transformation region expands at a constant speed, the strain field inside the inclusion is time-independent and uniform for uniform eigenstrain. Following the basic ideas of crack propagation problems in dynamic fracture mechanics, the reduction rate of the mechanical part of the free energy accompanying the growth of the transformation inclusion was derived as the driving force for the move of the interface. Then the equation to determine the propagation speed was established. It is found that there exists a steady speed for the growth of the transformation inclusion when time is approaching infinity. Finally the relation between the steady speed and the applied hydrostatic stress was derived explicitly.

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