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Estimations of Effective Energy-Based Criteria in Nonlinear Phenomena in Peridynamic Micromechanics of Random Structure Composites

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Abstract

One of the most important features of peridynamic modeling is a continuum description of material behavior as the summation of force interactions between material points. In contrast to local theory, 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. For random structure composite materials (CMs) under consideration, a linearized theory of bond-based peridynamics has been proposed before for multiphase constituents of arbitrary geometry. It is demonstrated that many nonlinear phenomena (e.g., plasticity, damage, and fatigue) in both local micromechanics and peridynamic ones are described by energy-based criteria, which, in turn, depend on the second moments of the local fields. Analyses of these nonlinear phenomena in peridynamics imply the availability of the direct numerical simulation that is only possible for CMs of deterministic structure (e.g., either a finite sample or periodic structure CMs). Considering random structure CMs with nonlinear phenomena is more complicated and requires some additional assumptions. The corresponding approaches in local micromechanics are well developed. The current study aims to bridge the gap between the linearized peridynamic micromechanics gathering momentum and a wide class of nonlinear phenomena for random structure CMs. It is performed by directly generalizing the concept of the field second moments (for energy-based criteria) previously developed in nonlinear local micromechanics to its peridynamic counterpart. Due to the identity (with accuracy to notations) of the operator forms of the new general integral equations (GIEs) of the local micromechanics and peridynamics of stochastic structural CMs, the proposed method is most advantageously applicable.

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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, 45202, OH, USA

    Valeriy A. Buryachenko

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Buryachenko, V.A. Estimations of Effective Energy-Based Criteria in Nonlinear Phenomena in Peridynamic Micromechanics of Random Structure Composites. J Peridyn Nonlocal Model (2023). https://doi.org/10.1007/s42102-023-00096-7

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