Basic sums and their random dynamic changes in description of microstructure of 2D composites

Mityushev, Vladimir; Nawalaniec, Wojciech

doi:10.1016/j.commatsci.2014.09.020

Cited by 24 publications

(6 citation statements)

References 25 publications

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“…The key point is a precise and convenient description of the geometrical set G which can be given, for instance, as a set of images. The recent research by Mityushev and Nawalaniec [5], where structural sums were applied in the systematic investigation of the dynami- cally changing structures, proposes a choice of the geometric parameters as the following set of structural sums: It is difficult to explicitly characterize the geometric meaning of the structural sums. The elements e m can be treated as weighted moments (integrals over the cell) of the correlation functions [2].…”

Section: Structural Sums and Geometrymentioning

confidence: 99%

“…The key point is a precise and convenient description of the geometrical set G which can be given, for instance, as a set of images. The recent research by Mityushev & Nawalaniec [5], where structural sums were applied in the systematic investigation of the dynamically changing structures, proposes a choice of the geometric parameters as the following set of structural sums:…”

Section: (C) Structural Sums and Geometrymentioning

confidence: 99%

“…It is worth noting the existing applications of structural sums in analysis of different kind of data. For example, Mityushev & Nawalaniec [5] used structural sums in the systematic investigation of dynamically changing microstructures. Other applications cover, for instance, an analysis of collective behaviour of bacteria [6], a description of random non-overlapping walks of discs on the plane [7] and parametrized comparison of composite materials obtained in different technological process [8].…”

Section: Introductionmentioning

confidence: 99%

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Classifying and analysis of random composites using structural sums feature vector

Nawalaniec

2019

Proc. R. Soc. A.

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The main goal of this paper is to present the application of structural sums, mathematical objects originating from the computational materials science, in construction of a feature space vector of 2D random composites simulated by distributions of non-overlapping disks on the plane. Construction of the feature vector enables the immediate application of machine learning tools and data analysis techniques to random structures. In order to present the accuracy and the potential of structural sums as geometry descriptors, we apply them to classification problems comprising composites with circular inclusions as well as composites with shapes formed by disks. As an application, we perform the analysis of different models of composites in order to formulate the irregularity measure of random structures. We also visualize the relationship between the effective conductivity of 2D composites and the geometry of inclusions.

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Section: Structural Sums and Geometrymentioning

confidence: 99%

Section: (C) Structural Sums and Geometrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Classifying and analysis of random composites using structural sums feature vector

Nawalaniec

2019

Proc. R. Soc. A.

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“…Geometric classifications of particle-reinforced composites can be based on the classification theory developed in [43] for dispersed inclusions. This theory uses the fundamental notion of the representative volume element (RVE) introduced in [44,45].…”

Section: Rve Theorymentioning

confidence: 99%

Cast aluminium matrix composites modified with using FSP process – Changing of the structure and mechanical properties

Kurtyka

Rylko

Tokarski

et al. 2015

Composite Structures

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“…The computationally effective formulae and algorithms for the absolutely convergent sums and ( > 2) were developed in [13,14]. However, the numerical implementation of the conditionally convergent series (74)-(75) for = 2 and (76) for = 3 requires further investigations.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Contrast Expansion Method for Elastic Incompressible Fibrous Composites

Drygaś

Mityushev

2017

Advances in Mathematical Physics

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Contrast parameter expansion of the elastic fields for 2D composites is developed by Schwarz's method and by the method of functional equations for the case of circular inclusions. A computationally efficient algorithm is described and implemented in symbolic form to compute the local fields in 2D elastic composites and the effective shear modulus for macroscopically isotropic composites. The obtained new analytical formula contains high-order terms in the contrast parameter and explicitly demonstrates dependence on the location of inclusions. As a numerical example, the hexagonal array is considered.

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Basic sums and their random dynamic changes in description of microstructure of 2D composites

Cited by 24 publications

References 25 publications

Classifying and analysis of random composites using structural sums feature vector

Classifying and analysis of random composites using structural sums feature vector

Cast aluminium matrix composites modified with using FSP process – Changing of the structure and mechanical properties

Contrast Expansion Method for Elastic Incompressible Fibrous Composites

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