On the shape of effective inclusion in the Maxwell homogenization scheme for anisotropic elastic composites

Sevostianov, Igor

doi:10.1016/j.mechmat.2014.03.003

Cited by 114 publications

(71 citation statements)

References 49 publications

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“…For example, Giraud and Sevostianov [19] used Maxwell scheme to calculate the effective elastic properties of a material containing randomly oriented concave superspherical pores. In the case of randomly oriented spheroids [11,20] …”

Section: Isotropic Distribution Of Identical Inhomogeneitiesmentioning

confidence: 99%

Maxwell Homogenization Scheme in Micromechanics: an Overview

Sevostianov

2017

MATEC Web Conf.

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Abstract. The paper discuss the classical Maxwell's (1873) homogenization method and the problems appearing in its practical implications. The method equates the far fields produced by a set of inhomogeneities and by a fictitious domain with unknown effective properties. It is re-written in terms of the property contribution tensors. The shape of the effective inclusion substantially affects the overall elastic properties. The choice of this shape in the case of anisotropic composite is a non-trivial problem. Another problem is related to the possible appearance of artificial singularities in the process of homogenization. We illustrate the method by several examples.

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Section: Isotropic Distribution Of Identical Inhomogeneitiesmentioning

confidence: 99%

Maxwell Homogenization Scheme in Micromechanics: an Overview

Sevostianov

2017

MATEC Web Conf.

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“…The authors discussed the uncertainty related to the shape of the effective inclusion but did not provide explicit recommendations regarding the choice of the shape in the general case. Sevostianov (2014) explicitly formulated the hypotheses that allow one to evaluate the shape of the effective inclusion. Kushch, Mogilevskaya, Stolarski, and Crouch (2012) verified these hypotheses numerically and illustrate, on simple examples, that approach proposed by Sevostianov (2014) allows one to optimize Maxwell's scheme.…”

Section: Maxwell Homogenization Scheme In Terms Of Property Contributmentioning

confidence: 99%

“…Approach developed by Sevostianov and Giraud (2013) and Sevostianov (2014) allows one to make this step. To obtain closed formulas, one has to know explicit expression for compliance contribution tensor of an inhomogeneity embedded in the anisotropic matrix.…”

Section: Maxwell Homogenization Scheme In Terms Of Property Contributmentioning

confidence: 99%

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Effective elastic properties of a particulate composite with transversely-isotropic matrix

Иванова

Sevostianov

2015

International Journal of Engineering Science

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“…Actually, the shrinkage porosity defects distributed irregularly in castings [1,11,17,18] , which means their configurations were intangible, and their shapes and spatial positions in casting were also somewhat different. Because of this inhomogeneous and random characteristic, the mechanical performances of castings with shrinkage porosity were uncertain [19,20] . Moreover, the crack growth behaviors were correlated with the probability distributions, such as the number (defect density), size, and location of defects [21,22] .…”

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Influence of random shrinkage porosity on equivalent elastic modulus of casting: A statistical and numerical approach

Liu

Yan³

et al. 2017

China Foundry

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L arge iron castings are widely used for "heavyduty" applications nowadays, such as wind/water generators or marine diesel engines. However, because of huge sections, complex shapes and numerous diecasts, shrinkage porosity defects cannot be totally eliminated in large castings [1,2] . In engineering, to avoid unnecessary waste, large castings with minor shrinkage defects are tolerable sometimes. But after all, shrinkage porosity is deleterious to casting components; it reduces the effective area for loading and results in stress concentration [3,4] . This conflict brings difficulties in material performance reliability evaluation and structural Abstract: Shrinkage porosity is a type of random distribution defects and exists in most large castings. Different from the periodic symmetry defects or certain distribution defects, shrinkage porosity presents a random "cloud-like" configuration, which brings difficulties in quantifying the effective performance of defected casting. In this paper, the influences of random shrinkage porosity on the equivalent elastic modulus of QT400-18 casting were studied by a numerical statistics approach. An improved random algorithm was applied into the lattice model to simulate the "cloud-like" morphology of shrinkage porosity. Then, a large number of numerical samples containing random levels of shrinkage were generated by the proposed algorithm. The stress concentration factor and equivalent elastic modulus of these numerical samples were calculated. Based on a statistical approach, the effects of shrinkage porosity's distribution characteristics, such as area fraction, shape, and relative location on the casting's equivalent mechanical properties were discussed respectively. It is shown that the approach with randomly distributed defects has better predictive capabilities than traditional methods. The following conclusions can be drawn from the statistical simulations: (1) the effective modulus decreases remarkably if the shrinkage porosity percent is greater than 1.5%; (2) the average Stress Concentration Factor (SCF) produced by shrinkage porosity is about 2.0; (3) the defect's length across the loading direction plays a more important role in the effective modulus than the length along the loading direction; (4) the surface defect perpendicular to loading direction reduces the mean modulus about 1.5% more than a defect of other position.

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On the shape of effective inclusion in the Maxwell homogenization scheme for anisotropic elastic composites

Cited by 114 publications

References 49 publications

Maxwell Homogenization Scheme in Micromechanics: an Overview

Maxwell Homogenization Scheme in Micromechanics: an Overview

Effective elastic properties of a particulate composite with transversely-isotropic matrix

Influence of random shrinkage porosity on equivalent elastic modulus of casting: A statistical and numerical approach

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