Uniqueness of Neutral Elastic Circular Nano-Inhomogeneities in Antiplane Shear and Plane Deformations

2016 ◽  
Vol 83 (10) ◽  
Author(s):  
Ming Dai ◽  
Peter Schiavone ◽  
Cun-Fa Gao
Keyword(s):  
Foreign Body ◽  
Stress Field ◽  
Antiplane Shear ◽  
Interface Effect ◽  
Interface Condition ◽  
External Loading ◽  
Surrounding Matrix ◽  
The Matrix ◽  
Interface Parameters ◽  
Plane Deformations

In elasticity theory, a neutral inhomogeneity is defined as a foreign body which can be introduced into a host solid without disturbing the stress field in the solid. The existence of circular neutral elastic nano-inhomogeneities has been established for both antiplane shear and plane deformations when the interface effect is described by constant interface parameters, and the surrounding matrix is subjected to uniform external loading. It is of interest to determine whether noncircular neutral nano-inhomogeneities can be constructed under the same conditions. In fact, we prove that only the circular elastic nano-inhomogeneity can achieve neutrality under these conditions with the radius of the inhomogeneity determined by the corresponding (constant) interface parameters and bulk elastic constants. In particular, in the case of plane deformations, the (uniform) external loading imposed on the matrix must be hydrostatic in order for the corresponding circular nano-inhomogeneity to achieve neutrality. Moreover, we find that, even when we relax the interface condition to allow for a nonuniform interface effect (described by variable interface parameters), in the case of plane deformations, only the elliptical nano-inhomogeneity can achieve neutrality.

An elastic harmonic inclusion near a rigid harmonic inclusion loaded by a couple

2019 ◽  
Vol 84 (3) ◽  
pp. 555-566
Author(s):  
Xu Wang ◽  
Liang Chen ◽  
Peter Schiavone
Keyword(s):  
Rigid Inclusion ◽  
Elastic Inclusion ◽  
Complex Loading ◽  
Solution Procedure ◽  
External Loading ◽  
Surrounding Matrix ◽  
The Matrix ◽  
Mapping Techniques ◽  
Loading Parameter ◽  
Harmonic Inclusion

AbstractWe use conformal mapping techniques to solve the inverse problem concerned with an elastic non-elliptical harmonic inclusion in the vicinity of a rigid non-elliptical harmonic inclusion loaded by a couple when the surrounding matrix is subjected to remote uniform stresses. Both a size-independent complex loading parameter and a size-dependent real loading parameter are introduced as part of the solution procedure. The stress field inside the elastic inclusion is uniform and hydrostatic; the interfacial normal and tangential stresses as well as the hoop stress on the matrix side are uniform along each one of the two inclusion–matrix interfaces. The tangential stress along the interface of the elastic inclusion (free of external loading) vanishes, whereas that along the interface of the rigid inclusion (loaded by the couple) does not. A novel method is proposed to determine the area of the rigid inclusion.

Uniform stress state inside a non-elliptical inhomogeneity near an irregularly shaped hole in antiplane shear

2019 ◽  
Vol 25 (2) ◽  
pp. 362-373 ◽  
Author(s):  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Antiplane Shear ◽  
Shear Stresses ◽  
Uniform Stress ◽  
Elliptical Inhomogeneity ◽  
Surrounding Matrix ◽  
The Matrix ◽  
Shaped Hole ◽  
Mapping Techniques ◽  
Hole Boundary ◽  
High Level

Analytic continuation and conformal mapping techniques are applied to establish that the state of stress inside a non-elliptical elastic inhomogeneity can remain uniform despite the presence of a nearby irregularly shaped hole when the surrounding matrix is subjected to uniform remote antiplane shear stresses. The hole boundary is assumed to be either traction-free or subjected to antiplane line forces. Detailed numerical results are presented to demonstrate the resulting analytical solutions. Our results indicate that in maintaining a uniform stress distribution inside the inhomogeneity, it is permissible for the stresses in the matrix to exhibit either a square root singularity at sharp corners of a hole boundary or a high level of stress concentration at rounded corners of a hole.

A circular Eshelby inclusion interacting with a non-parabolic open inhomogeneity with internal uniform anti-plane stresses

2019 ◽  
Vol 25 (3) ◽  
pp. 573-581 ◽  
Author(s):  
Xu Wang ◽  
Ping Yang ◽  
Peter Schiavone
Keyword(s):  
Stress Field ◽  
Conformal Mapping ◽  
Stress Distributions ◽  
Uniform Stress ◽  
Elastic Deformations ◽  
Surrounding Matrix ◽  
Eshelby Inclusion ◽  
The Matrix ◽  
Uniform Stress Field ◽  
Mapping Techniques

Using conformal mapping techniques and analytic continuation, we prove that when subjected to anti-plane elastic deformations, a non-parabolic open inhomogeneity continues to admit an internal uniform stress field when a circular Eshelby inclusion is placed in its vicinity and the surrounding matrix is subjected to uniform remote stresses. Explicit expressions for the non-uniform stress distributions in the matrix and in the circular Eshelby inclusion are obtained. The internal uniform stress field is independent of the shape of the inhomogeneity and the presence of the circular Eshelby inclusion, whereas the existence of the circular Eshelby inclusion exerts a significant influence on the shape of the non-parabolic open inhomogeneity as well as on the non-uniform stress distributions in the matrix and in the circular Eshelby inclusion itself.

ANALYSIS OF PROTEOGLYCAN GENE EXPRESSION IN CONNECTIVE TISSUES BY SEMI-QUANTITATIVE RT-PCR

2001 ◽  
Vol 05 (02) ◽  
pp. 79-88
Author(s):  
K. Dobra ◽  
A. Hjerpe
Keyword(s):  
Rt Pcr ◽  
Connective Tissues ◽  
Surrounding Matrix ◽  
Cell Proliferation And Differentiation ◽  
Extracellular Matrix Components ◽  
Proliferation And Differentiation ◽  
The Matrix ◽  
Quantitative Changes ◽  
Regulatory Functions ◽  
Multiple Samples

Proteoglycans (PGs) are cell-membrane and extracellular matrix components with a wide variety of different functions. In the matrix, they are mainly of structural importance, although some of them have been ascribed specific regulatory functions, such as in the assembly of collagen fibers. PGs on the cell surface act as essential modulators of specific ligand-binding reactions, involving interactions between adjacent cells and between cells and surrounding matrix. Through these interactions they participate in different processes, including cell proliferation and differentiation. Qualitative and quantitative changes in PG expression can therefore be associated with various physiological and pathological conditions. We have optimized the conditions for semi-quantitative evaluation of proteoglycan expression by RT-PCR reaction, using glyceraldehyde-3-phosphate dehydrogenase (GAPDH) as reference gene. The relative fluorescence of analyte to reference amplimers can — within certain limits — be used to estimate the amount of target RNA and allows direct comparison of multiple samples. The profile of PG expression obtained in this way can be used to extend our current understanding of the possible functions that can be associated with these complex molecules.

Histologic Study of Homograft Cartilages Implanted in the Middle Ear

1988 ◽  
Vol 98 (6) ◽  
pp. 546-551 ◽  
Author(s):  
Etsuo Yamamoto ◽  
Michitaka Iwanaga ◽  
Manabu Fukumoto
Keyword(s):  
Foreign Body ◽  
Connective Tissue ◽  
Middle Ear ◽  
Foreign Body Reaction ◽  
Fibrous Connective Tissue ◽  
Histologic Study ◽  
Second Stage ◽  
The Matrix ◽  
Inflammatory Changes ◽  
Histologic Changes

We examined conditions of the micro-sliced homograft cartilages implanted in the middle ear, implanted cartilages removed at revision surgery or implanted cartilages removed at the second stage of staged tympanoplasty, both macroscopically and histologically. Macroscopically, the appearance and shape of the cartilages remained unchanged, with no evidence of erosion. There was no evidence of any foreign body reaction or rejection phenomenon. In general, no marked histologic changes of the matrix tissues were found, although chondrocytes showed degenerative changes. There was partial absorption of cartilage and replacement by fibrous connective tissue when inflammatory changes occurred in the middle ear. It is concluded that implanted homograft cartilage maintains its stiffness for more than 6 months in a healthy, aerated middle ear and appears to be clinically useful for tympanoplasty.

Plane Deformations of an Inhomogeneity–Matrix System Incorporating a Compressible Liquid Inhomogeneity and Complete Gurtin–Murdoch Interface Model

2018 ◽  
Vol 85 (12) ◽  
Author(s):  
Ming Dai ◽  
Min Li ◽  
Peter Schiavone
Keyword(s):  
Analytic Solution ◽  
Elastic Solid ◽  
Compressible Liquid ◽  
External Loading ◽  
Interface Model ◽  
Interface Tension ◽  
Soft Solids ◽  
Remote Loading ◽  
Interface Elasticity ◽  
Plane Deformations

We consider the plane deformations of an infinite elastic solid containing an arbitrarily shaped compressible liquid inhomogeneity in the presence of uniform remote in-plane loading. The effects of residual interface tension and interface elasticity are incorporated into the model of deformation via the complete Gurtin–Murdoch (G–M) interface model. The corresponding boundary value problem is reformulated and analyzed in the complex plane. A concise analytical solution describing the entire stress field in the surrounding solid is found in the particular case involving a circular inhomogeneity. Numerical examples are presented to illustrate the analytic solution when the uniform remote loading takes the form of a uniaxial compression. It is shown that using the simplified G–M interface model instead of the complete version may lead to significant errors in predicting the external loading-induced stress concentration in gel-like soft solids containing submicro- (or smaller) liquid inhomogeneities.

A New Method to Measure the Microresidual Stress-Field Around Inclusions

1968 ◽  
Vol 90 (4) ◽  
pp. 620-622 ◽  
Author(s):  
L. B. Gulbransen ◽  
S. K. Chatterjee
Keyword(s):  
Free Energy ◽  
Domain Wall ◽  
Stress Field ◽  
Domain Walls ◽  
Manganese Sulfide ◽  
Ferromagnetic Material ◽  
New Method ◽  
The Matrix

A brief review of various theories of interaction of inclusions and domain walls in a ferromagnetic material is presented. A postulate concerning the modification of domain patterns by inclusions, based on theory, is described and the various free-energy contributions of the inclusion to the matrix in the vicinity of the inclusion are discussed. Examples of domain wall bending in ingot iron by manganese sulfide inclusions are shown to agree with the postulated model of interaction of a stress field around the inclusion and the domain wall.

Use of automated photoelasticity to determine stress intensity factors of bimaterial joints

2005 ◽  
Vol 40 (8) ◽  
pp. 785-800 ◽  
Author(s):  
B Zuccarello ◽  
S Ferrante
Keyword(s):  
Stress Intensity ◽  
Stress Field ◽  
Stress Intensity Factors ◽  
External Loading ◽  
Intensity Factors ◽  
Singular Stress ◽  
Full Field ◽  
Basic Law ◽  
Singular Stress Field ◽  
Element Approach

A new systematic experimental procedure has been developed to obtain the stress intensity factors governing the singular stress field that occurs near the intersection between the interface and free edges of bimaterial joints. A preliminary theoretical study of the singular stress field is carried out by the well-known Airy stress function method. The obtained stress laws are properly combined with the basic law of photoelasticity in order to define a procedure that permits the zone dominated by the singularity to be located and the stress intensity factors (SIFs) to be computed on the basis of full field data provided from automated photoelasticity. In particular, a systematic error analysis is used to determine the model zone where the experimental data have to be collected in order to obtain accurate SIF evaluation. As an example, the proposed method is applied to determine the SIFs of various aluminium/ PSM-1 specimens under different external loading conditions using Fourier transform photoelasticity. The experimental results have been compared to those obtained by an independent procedure, based on a boundary element approach, in order to validate the accuracy of the proposed procedure.

Residual strain energy in composites containing particles

1996 ◽  
Vol 11 (2) ◽  
pp. 483-494 ◽  
Author(s):  
Toshiaki Mizutani
Keyword(s):  
Strain Energy ◽  
Crystal Lattices ◽  
Composite Systems ◽  
Surrounding Matrix ◽  
Dispersed Particles ◽  
First Approximation ◽  
Bulk Stress ◽  
The Matrix ◽  
Unit Cells ◽  
Physical Validity

Selsing's formula for radial tension at the particle-matrix interface is extended into a general formula which includes the effects of the amount of dispersed particles. A relationship is derived between individual volumes of strained unit cells in the crystal lattices of the particles and of the surrounding matrix. These relationships are used to predict the effect of the particles (2H−TiB2, 2H−ZrB2, and t−WB) on their unit cells and on the unit cell of the surrounding 6H–SiC matrix. The precision of these predictions was 7.1% or better. Hence, in principle, it is possible to investigate the distributions of residual bulk stress/strain. Estimates of characterizing values of the three composite systems are attempted on the rough basis of the elastic constants of the SiC matrix, confirming the physical validity of this approach as a first approximation. Further, the residual bulk strain energies of the particles and the matrix are discussed in connection with the elastic term involved in the fracture energy of such composites.

Buckling of Microfibers

1967 ◽  
Vol 34 (4) ◽  
pp. 1011-1016 ◽  
Author(s):  
M. A. Sadowsky ◽  
S. L. Pu ◽  
M. A. Hussain
Keyword(s):  
Elevated Temperatures ◽  
Thermal Characteristics ◽  
Compressive Force ◽  
Theory Of Elasticity ◽  
Primary Objective ◽  
Infinite Length ◽  
Volume Percentage ◽  
Initial Strength ◽  
Surrounding Matrix ◽  
The Matrix

Most composites are fabricated at elevated temperatures and cooled to room temperature. The difference in coefficients of thermal expansion of the fiber and matrix may cause buckling of the slender-shaped microfibers. This would greatly reduce the initial strength of the composites. The primary objective of this paper is to explain qualitatively the basic phenomenon of buckled microfibers in a composite and to present some numerical results in certain ranges of elastic parameters. Our analysis is based on assumptions that (a) the volume percentage of fibers is small so that the mutual interference of fibers is negligible and the matrix surrounding a fiber may be considered as infinitely large; (b) the diameter of the fiber is very small in comparison to its length so that the fiber may be treated as a linear fiber with infinite length; (c) the constituents are homogeneous and isotropic and the classical linear theory of elasticity may be applied; and, (d) in the process of cooling, the fiber is subjected to compression but not twisting moment by the surrounding matrix. The analysis leads to a relation between the pertinent elastic and thermal characteristics of the matrix and microfiber and the compressive force along the axis of the microfiber at the critical moment of incipient buckling. With the knowledge of that relation, it is now possible to know in advance whether or not buckling is to be expected and to avoid such manufacturing methods in which a threat of having buckled microfibers is present.

Sign in / Sign up

Export Citation Format

Share Document