Combining Maxwell’s methodology with the BEM for evaluating the two-dimensional effective properties of composite and micro-cracked materials

Mogilevskaya, Sofia G.; Crouch, Steven L.

doi:10.1007/s00466-012-0735-5

Cited by 16 publications

(9 citation statements)

References 43 publications

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“…(3.1)). This case is similar to the work from the complex variable BEM [13]. Original Maxwell homogeneous method for calculating electric conduction did not consider the interaction between inhomogeneities [12].…”

Section: ð3:5þmentioning

confidence: 78%

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An interface integral formulation of heat energy calculation of steady state heat conduction in heterogeneous media

Dong

2015

International Journal of Heat and Mass Transfer

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Section: ð3:5þmentioning

confidence: 78%

“…In the present work, we follow the method of [13], i.e. the effective inclusion with the interface C is assumed to be a circle (2D) or a sphere (3D) with radius a.…”

Section: ð3:5þmentioning

confidence: 99%

An interface integral formulation of heat energy calculation of steady state heat conduction in heterogeneous media

Dong

2015

International Journal of Heat and Mass Transfer

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“…The boundary value problem is solved by means of the complex variables boundary element code described in (45). The elastic properties K * c , μ c can be evaluated using the approach suggested in (19,20). The new elastic properties, K * in 1 , (μ in ) 1 obtained from (5.2), (5.5) and (5.8) are then used in the next iteration.…”

Section: Interpretation Of the Equations Of Section 5 And 'Strange' Pmentioning

confidence: 99%

“…This analysis leads to the discovery of some remarkable properties of regular polygonal and other symmetric inhomogeneities. In Section 7, employing the interrelations obtained in Sections 4 and 5 and the results on the effective properties obtained in (19,20) (with the use of the circular equivalent inhomogeneity), we recalculate the effective transverse elastic properties for the materials with hexagonal structure. We demonstrate that these new estimates do not diverge with the size of the cluster unlike the corresponding circular inhomogeneity-based estimates.…”

Section: Introductionmentioning

confidence: 99%

The shape of Maxwell's equivalent inhomogeneity and ‘strange’ properties of regular polygons and other symmetric domains

Mogilevskaya

Nikolskiy

2015

Q J Mechanics Appl Math

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The Maxwell concept of equivalent inhomogeneity is reexamined in the context of elastic composite, porous or micro-cracked materials of periodic structure. It is demonstrated that accurate estimates for the effective elastic properties can be obtained by the modified Maxwell approach that employs the proper shape of the equivalent inhomogeneity and explicitly accounts for the geometry of the cluster and for the interactions between its constituents. In addition, it is shown that regular polygonal and some other symmetric inhomogeneities possess 'strange'and remarkable properties. Under the action of uniform far-field loads, the averages of certain combinations of stresses inside these inhomogeneities are constant and coincide with those for a circular inhomogeneity.

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“…Kaminski [1999] employed the boundary element formulationsbased homogenization to deal with the periodic transversely isotropic linear elastic fiber-reinforced composites. Besides, Maxwell's methodology was combined with the complex-variable BEM for evaluating the two-dimensional effective elastic properties of composites with periodic or random fibers, pores, or cracks, provided that the overall behavior is isotropic, and inclusions'effects are assumed to be the same as those of an equivalent circular inhomogeneity [Mogilevskaya and Crouch (2013)]. …”

Section: Introductionmentioning

confidence: 99%

Special Elements for Composites Containing Hexagonal and Circular Fibers

Qin

2015

Int. J. Comput. Methods

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In this paper, unidirectional fiber reinforced composites with periodic square array of circular and hexagonal fibers is studied by a novel fundamental-solution-based hybrid finite element model. Due to the periodicity of composites, a representative unit cell containing a single fiber with circular or hexagonal cross section is taken into consideration and analyzed using the proposed hybrid finite element model. In the present numerical model, special polygonal fiber elements with arbitrary number of sides are developed by coupling the independent element interior and frame displacement fields. The element interior displacement fields are approximated by the combination of fundamental solutions to prior satisfy the governing equation of the problem, so that the domain integral appeared in the weak-form hybrid functional in terms of dual variables is converted into boundary integrals. Independently the element frame displacement fields are approximated by the conventional shape functions to guarantee the continuity of adjacent elements. Following this, special polygonal fiber elements are constructed to reduce mesh effort in the fiber region and achieve good accuracy with fewer elements. Finally, numerical tests are carried out for assessing the performance of the present special elements.

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Combining Maxwell’s methodology with the BEM for evaluating the two-dimensional effective properties of composite and micro-cracked materials

Cited by 16 publications

References 43 publications

An interface integral formulation of heat energy calculation of steady state heat conduction in heterogeneous media

An interface integral formulation of heat energy calculation of steady state heat conduction in heterogeneous media

The shape of Maxwell's equivalent inhomogeneity and ‘strange’ properties of regular polygons and other symmetric domains

Special Elements for Composites Containing Hexagonal and Circular Fibers

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