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Elastic Homogenization of Materials with Composite Network Structures

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We extend the method of maximal advance paths to the case of elastic homogenization of materials with composite network microstructure. Some distributions of the vectors of stretching of the links for each component are introduced in the representations of network microstrains. On the basis of the refined statistics of orientations of links in the maximal advance paths, we obtain a new formulation of the kinematic relation connecting these micromechanical variables with macroscopic strains in the material. The problem of determination of the network balance is solved by the intermediate averaging of strains and the response of links with identical initial orientations. As a result, different components of the network are replaced with an equivalent link. Within the framework of the proposed model, we establish the series character of their joining and the transmission of forces in the network. We also analyze the qualitative differences in the behaviors of materials with different structures, which can be explained by the geometric and physical properties of elements of the composite network microstructures.

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Authors and Affiliations

  1. “Kharkiv Polytechnic Institute” National Technical University, Kharkiv, Ukraine

    М. М. Тkachuk

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  1. М. М. Тkachuk
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Correspondence to М. М. Тkachuk.

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 62, No. 3, pp. 92–105, July–September, 2019.

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Тkachuk, М.М. Elastic Homogenization of Materials with Composite Network Structures. J Math Sci 263, 104–119 (2022). https://doi.org/10.1007/s10958-022-05910-z

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