On elastic interactions between spherical inclusions by the equivalent inclusion method

Benedikt, B.; Lewis, Matthew W.; Rangaswamy, P.

doi:10.1016/j.commatsci.2005.10.002

Cited by 23 publications

(17 citation statements)

References 18 publications

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“…It should be mentioned that the sharp strain gradient at the interface between the inclusion and the matrix as pointed out by Benedikt et al (2006) is not considered by the Eshelby's equivalent inclusion method. It affects a very small volume in the vicinity of the interface that may modify the solution for interacting inclusions when they are very close each other.…”

Section: Fig 5 Presents the Dimensionless Contact Pressure Distributionmentioning

confidence: 97%

Contact analysis in presence of spherical inhomogeneities within a half-space

Leroux

Fulleringer

Nélias

2010

International Journal of Solids and Structures

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a b s t r a c tThis paper presents a fast method of solving contact problems when one of the mating bodies contains multiple heterogeneous inclusions, and numerical results are presented for soft or stiff inhomogeneities. The emphasis is put on the effects of spherical inclusions on the contact pressure distribution and subsurface stress field in an elastic half-space. The computing time and allocated memory are kept small, compared to the finite element method, by the use of analytical solution to account for the presence of inhomogeneities. Eshelby's equivalent inclusion method is considered in the contact solver. An iterative process is implemented to determine the displacements and stress fields caused by the eigenstrains of all spherical inclusions. The proposed method can be seen as an enrichment technique for which the effect of heterogeneous inclusions is superimposed on the homogeneous solution in the contact algorithm. 3D and 2D Fast Fourier Transforms are utilized to improve the computational efficiency. Configurations such as stringer and cluster of spherical inclusions are analyzed. The effects of Young's modulus, Poisson's ratio, size and location of the inhomogeneities are also investigated. Numerical results show that the presence of inclusions in the vicinity of the contact surface could significantly changes the contact pressure distribution. From a numerical point of view the role of Poisson's ratio is found very important. One of the findings is that a relatively 'soft' and nearly incompressible inclusion -for example a cavity filled with a liquid -can be more detrimental for the stress state within the matrix than a very hard inclusion with a classical Poisson's ratio of 0.3. Ó

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Section: Fig 5 Presents the Dimensionless Contact Pressure Distributionmentioning

confidence: 97%

Contact analysis in presence of spherical inhomogeneities within a half-space

Leroux

Fulleringer

Nélias

2010

International Journal of Solids and Structures

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“…Therefore, the zoom factor A defined in Eq . 3 can be divided in to three forms ( A N , A S , and A T ): To analyze the stress distribution of cohesive layer under these basic loading cases, an improved EIM presented in [21] is used.…”

Section: Prediction Of the Cohesive Strengthmentioning

confidence: 99%

“…In [21], it has been numerically demonstrated that even the solution of EIM consistency equations with constant eigenstrains could be used to obtain fairly accurate stress distributions, if the position of the expansion point x p is allowed to follow the locations where the stress field is computed. In this article, for simplicity, only the constant eigenstrains are assumed in the consistency equations.…”

Section: Prediction Of the Cohesive Strengthmentioning

confidence: 99%

“…In this model, the cohesive strength is considered dependent on the stress concentrations induced by fiber inclusions in cohesive layer. An improved EIM proposed by Benedikt et al [21] is applied to find the stress distribution around interacting inclusions. Furthermore, FEM simulations on MMB and six‐point bending test are presented to corroborate this model.…”

Section: Introductionmentioning

confidence: 99%

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Prediction of the strength parameter of cohesive zone model for simulating composite delamination by the equivalent inclusion method

Chen

2011

Polymer Composites

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The cohesive strength is an important parameter in numerically modeling composite delamination via cohesive zone model‐based FEM. A micromechanical model is proposed to predict the cohesive strength based on Eshelby's equivalent inclusion method (EIM). In this model, it is considered that the cohesive strength depends heavily on the stress concentrations at the microscopic level. The cohesive strengths of T700/QY8911 and AS4/PEEK laminates at various cross‐angles of the bidirectional fibers are computed using EIM with constant eigenstrains. With the predicted cohesive strengths the FEM simulations on mixed‐mode bending and six‐point bending test are presented, and the results are in fair agreement with experimental observation. POLYM. COMPOS., 2011. © 2011 Society of Plastics Engineers

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“…The seminal work was done by Moschovidis and Mura 15, who studied two non‐intersecting ellipsoidal inhomogeneities by approximating the equivalent eigenstrains with a Taylor series. Other works that concern non‐intersecting inhomogeneities include the studies of two spherical inhomogeneities 16, a penny‐shaped crack interacting with a spherical inhomogeneity 17, 18, and multiple spherical inhomogeneities 19. The double‐inhomogeneity problem in which one inhomogeneity is surrounded by another was investigated to simulate a single coated particle/fiber embedded in a matrix 20.…”

Section: Introductionmentioning

confidence: 99%

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

Zhou

Keer

Wang

2011

Numerical Meth Engineering

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SUMMARYThis paper develops a semi-analytic solution for multiple arbitrarily shaped three-dimensional inhomogeneous inclusions embedded in an infinite isotropic matrix under external load. All interactions between the inhomogeneous inclusions are taken into account in this solution. The inhomogeneous inclusions are discretized into small cuboidal elements, each of which is treated as a cuboidal inclusion with initial eigenstrain plus unknown equivalent eigenstrain according to the Equivalent Inclusion Method. All the unknown equivalent eigenstrains are determined by solving a set of simultaneous constitutive equations established for each equivalent cuboidal inclusion. The final solution is obtained by summing up the closed-form solutions for each individual equivalent cuboidal inclusion in an infinite space. The solution evaluation is performed by application of the fast Fourier transform algorithm, which greatly increases the computational efficiency. Finally, the solution is validated by taking Eshelby's analytic solution of an ellipsoidal inhomogeneous inclusion as a benchmark and by the finite element analysis. A few sample results are also given to demonstrate the generality of the solution. The solution may have potentially significant applications in solving a wide range of inhomogeneity-related problems.

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On elastic interactions between spherical inclusions by the equivalent inclusion method

Cited by 23 publications

References 18 publications

Contact analysis in presence of spherical inhomogeneities within a half-space

Contact analysis in presence of spherical inhomogeneities within a half-space

Prediction of the strength parameter of cohesive zone model for simulating composite delamination by the equivalent inclusion method

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

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