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Transformation Field Analysis and Clustering Discretization Method in Peridynamic Micromechanics of Composites

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Abstract

In contrast to the classical local theories, the peridynamic equation of motion introduced by Silling (J Mech Phys Solids 48:175–209, 2000) is free of any spatial derivatives of the displacement field. A theory of thermoelastic composite materials (CMs) with nonlocal peridynamic properties of multiphase constituents of arbitrary geometry is analyzed for periodic structure CMs subjected to the volumetric periodic boundary conditions. At first, we consider a linear thermoelastic problem for perydynamics CMs. Effective properties of peridynamic CM are expressed through the introduced micro polarization tensor averaged over the extended inclusion phase. Decompositions of material and field parameters are performed for analysis of the fields produced by both mechanical loading and eigenfield loading. Transformation field analysis (TFA) and clustering discretization method (defining offline linear stage) adapted to the linear peridynamic micromechanics are proposed (the novelty of the approach proposed) by the use of formal similarity of suggested methods with corresponding approaches of local micromechanics (LM). Stress and displacement in each cluster are assumed to be constant and linear functions, respectively, even when a cluster is not a simply connected area in general. This fact greatly reduces the degree of freedom in the problem being considered and leads to a greatly improved computational efficiency with their wide potential applications (e.g., in machine learning). The clustering version of TFA for the homogenization of nonlinear elastic peridynamic micromechanics (PM, online nonlinear stage) is based on employing eigenstrains to account for inelastic displacements arising from material nonlinearity. The scheme of numerical solution of linear thermoelastic peridynamic problem and estimation of influence functions are presented.

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Acknowledgements

The author acknowledges Dr. Stewart A. Silling for the fruitful personal discussions, encouragements, helpful comments, and suggestions. The author also acknowledges the reviewers for the encouraging comments that initiated a significant correction of the manuscript.

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  1. Micromechanics & Composites LLC, Cincinnati, OH, 45202, USA

    Valeriy A. Buryachenko

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Buryachenko, V.A. Transformation Field Analysis and Clustering Discretization Method in Peridynamic Micromechanics of Composites. J Peridyn Nonlocal Model (2024). https://doi.org/10.1007/s42102-023-00113-9

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