Semi‐analytic solution for multiple interacting three‐dimensional inhomogeneous inclusions of arbitrary shape in an infinite space

Zhou, Kun; Keer, Leon M.; Wang, Q. Jane

doi:10.1002/nme.3117

Cited by 93 publications

(24 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…14) In addition, the inhomogeneous problem (the elastic constant of the inclusion differs from the matrix) can be solved by an equivalent inclusion method based on the Eshelby's treatment. 11,15) The above method is capable of calculating elastic field (strain and stress) of the system containing single and multiple homogenous/inhomogeneous inclusions.…”

Section: )mentioning

confidence: 99%

On the Elastic Accommodation Between the Structural Units in the LPSO Structures

2014

Mater. Trans.

View full text Add to dashboard Cite

Long range periodic stacking ordered (LPSO) structures in magnesium alloy consist of regular arrangements of four layer height fcc structural units separated by several Mg layers paralleling to the base plane. The shear transformation of the structural units from hcp structure involves large transformation strain. This strain can be significantly accommodated by the combination of the structure units with different shears. In addition, the possible lowest elastic energy configuration in both R and H type of LPSO structure is obtained. For H type LPSO structure, the opposite shear directions (or Burgers vectors of the partial dislocations) are operated in nearest structural units, while all three types of shear directions are operated successively in the nearest structural units for R type LPSO structure. This study also intends to discuss the inter spacing between the structural units in terms of the elastic interaction. It is found the elastic interaction alone cannot rationalize the spacing between the structural units.

show abstract

Section: )mentioning

confidence: 99%

On the Elastic Accommodation Between the Structural Units in the LPSO Structures

2014

Mater. Trans.

View full text Add to dashboard Cite

show abstract

“…It is chiefly down to individual preference although it is important to note that Hill's tensor possesses the major symmetries whereas Eshelby's does not in general. Some find the notion of eigenstrain rather artificial, although in many cases it is a very useful concept as a means for solving harder problems such as the case of multiple inhomogeneities [79], [124]. The simple relation S = PC 0 (1.1) between the Hill (P) and Eshelby (S) tensor, where C 0 is the host modulus tensor, means that deriving one immediately yields the other.…”

Section: Introductionmentioning

confidence: 99%

The Eshelby, Hill, Moment and Concentration Tensors for Ellipsoidal Inhomogeneities in the Newtonian Potential Problem and Linear Elastostatics

Parnell

2016

J Elast

View full text Add to dashboard Cite

One of the most cited papers in Applied Mechanics is the work of Eshelby from 1957 who showed that a homogeneous isotropic ellipsoidal inhomogeneity embedded in an unbounded (in all directions) homogeneous isotropic host would feel uniform strains and stresses when uniform strains or tractions are applied in the far-field. Of specific importance is the uniformity of Eshelby's tensor S. Following Eshelby's seminal work, a vast literature has been generated using and developing Eshelby's result and ideas, leading to some beautiful mathematics and extremely useful results in a wide range of application areas. In 1961 Eshelby conjectured that for anisotropic materials only ellipsoidal inhomogeneities would lead to such uniform interior fields. Although much progress has been made since then, the quest to prove this conjecture is still not complete; numerous important problems remain open. Following a different approach to that considered by Eshelby, a closely related tensor P = SD 0 arises, where D 0 is the host medium compliance tensor. The tensor P is associated with Hill and is of course also uniform when ellipsoidal inhomogeneities are embedded in a homogeneous host phase. Two of the most fundamental and useful areas of applications of these tensors are in Newtonian potential problems such as heat conduction, electrostatics, etc. and in the vector problems of elastostatics. Knowledge of the Hill and Eshelby tensors permit a number of interesting aspects to be studied associated with inhomogeneity problems and more generally for inhomogeneous media. Micromechanical methods established mainly over the last half-century have enabled bounds on and predictions of the effective properties of composite media. In many cases such predictions can be explicitly written down in terms of the Hill tensor, or equivalently the Eshelby tensor and can be shown to provide excellent predictions in many cases.Of specific interest is that a number of important limits of the ellipsoidal inhomogeneity can be taken in order to be employed in predictions of the effective properties of, for example, layered media and fibre reinforced composites and also to the cases when voids and cracks are present. In the main, results for the Hill and Eshelby tensors are distributed over a wide range of articles and books, using different notation and terminology and so it is often difficult to extract the necessary information for the tensor that one requires. The case of an anisotropic host phase is also frequently non-trivial due to the requirement of the associated Green's tensor. Here this classical problem is revisited and a large number of results for problems that are felt to be of great utility in a wide range of disciplines are derived or recalled. A scaling argument leads to the derivation of the Eshelby tensor for potential problems where the host phase is at most orthotropic, without the requirement of using the anisotropic Green's function. The Concentration tensor A linking interior fields to those imposed in the far-field is de...

show abstract

“…According to the obtained pressure, (3) and (4) are computed for getting the stress and displacement of the frustule. For this, the finite element method is usually employed due to the complexity in the porous frustule of the diatom, although there are other efficient methods for computing solid performances such as FFT one [21][22][23]. When the displacement is obtained, it, as boundary input, is transmitted to (1) and (2) and then repeat the above solution process until the given convergent standards are met.…”

Section: Governing Equationsmentioning

confidence: 99%

Investigation of Tribological Performances for Porous Structure of Diatom Frustule with FSI Method

Meng

Gao

2014

Advances in Condensed Matter Physics

View full text Add to dashboard Cite

Tribological performances of the diatom frustule are investigated with the liquid-solid interaction (FSI) method. Take, for example, the representativeCoscinodiscussp. shell; the diatom frustule with the porous structure is achieved by the scanning electron microscope (SEM). Based on the frustule, the representative diatom frustule is modeled. Further, tribological performances of the diatom at its different geometry sizes and velocities are solved with FSI method and compared with corresponding values for the nonporous structure. The numerical result shows that the existence of the porous structure of the diatom helps to reduce friction between it and ambient water and to increase its load-carrying capacity.

show abstract

Semi‐analytic solution for multiple interacting three‐dimensional inhomogeneous inclusions of arbitrary shape in an infinite space

Cited by 93 publications

References 52 publications

On the Elastic Accommodation Between the Structural Units in the LPSO Structures

On the Elastic Accommodation Between the Structural Units in the LPSO Structures

The Eshelby, Hill, Moment and Concentration Tensors for Ellipsoidal Inhomogeneities in the Newtonian Potential Problem and Linear Elastostatics

Investigation of Tribological Performances for Porous Structure of Diatom Frustule with FSI Method

Contact Info

Product

Resources

About