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Unified Micromechanics of Matrix Composites

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Abstract:

Due to the identical operator form of general integral equations (GIE) proposed for both local micromechanics (LM) and a wide class of nonlocally elastic [weakly nonlocal (strain-gradient, stress-gradient) and strongly nonlocal (strain type and displacement type, peridynamics). The modified computational analytical micromechanics (CAM) approach is built on an exact Additive General Integral Equation (AGIE), applicable to CMs with a wide class of structural configuration and phase behavior. A unified iterative solution to the static AGIE is developed, using a compactly supported body force as a fundamentally new training parameter. The method introduces an extended Representative Volume Element concept that generalizes Hill's classical framework. The AGIE-CAM framework enables seamless integration with machine learning (ML) and neural network (NN) methods for constructing any unpredefined surrogate nonlocal operators. The methodology is designed as a modular, block-based system, supporting flexible development and refinement of computational tools.

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Periodical:

Key Engineering Materials (Volume 1033)

Pages:

73-79

DOI:

https://doi.org/10.4028/p-3uPxxI

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Cite this paper

Online since:

November 2025

Authors:

Valeriy Buryachenko*

Keywords:

Microstructures, Multiscale Modeling, Non-Local Methods, Peridynamics

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© 2025 Trans Tech Publications Ltd. All Rights Reserved

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References

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