arXiv subjects

Valeriy A. Buryachenko

Publications and source records attributed to Valeriy A. Buryachenko.

7 recordsLinked to original sources

arXiv2025

New RVE concept and FFT methods in micromechanics of composites subjected to body force with compact support

We consider static linear elastic composite materials (CMs) with periodic structure. The core of the proposed methodology is the generation of a novel dataset using specially designed body force fields with compact support (BFCS), enabling a new RVE concept that reduces the infinite periodic medium to a finite domain without boundary artifacts. This functionally reduced RVE is used for translated averaging of direct numerical simulations (DNS) results, efficiently computed via a newly developed FFT-based solver for BFCS loading. The resulting dataset captures localized field responses and is used to train machine learning (ML) and neural networks (NN) models to learn effective nonlocal surrogate operators. These operators accurately predict macroscopic responses while reflecting microstructural features and nonlocal interactions. By accounting for field localization while simultaneously eliminating influences from finite sample size and boundary effects, it provides a physically grounded and data-driven framework for constructing accurate surrogate models for the homogenization of complex materials.

physics.comp-ph↗

arXiv2025

Unified Micromechanics Theory of Composites

We consider the matrix composite materials (CM) of either random (statistically homogeneous or inhomogeneous), periodic, or deterministic (neither random nor periodic) structures. CMs exhibit linear or nonlinear behavior, coupled or uncoupled multi-physical phenomena, locally elastic, weakly nonlocal (strain gradient and stress gradient), or strongly nonlocal (strain-type and displacement-type, peridynamics) phase properties. A modified Computational Analytical Micromechanics (CAM) approach introduces an exact Additive General Integral Equation (AGIE) for CMs of any structure and phase properties mentioned above. The unified iteration solution of static AGIEs is adapted to the body force with compact support serving as a fundamentally new universal training parameter. The approach also establishes a critical threshold for filtering out unsuitable sub-datasets of effective parameters through a novel Representative Volume Element (RVE) concept, which extends Hill's classical framework. This RVE concept eliminates sample size, boundary layer, and edge effects, making it applicable to CMs of any structure and phase properties, regardless of local or nonlocal, linear or nonlinear. Incorporating this new RVE concept into machine learning and neural network techniques enables the construction of any unpredefined surrogate nonlocal operators. The methodology is structured as a modular, block-based framework, allowing independent development and refinement of software components. This flexible, robust AGIE-CAM framework integrates data-driven, multi-scale, and multi-physics modeling, accelerating research in CM of any microtopology and phase properties considered. The AGIE-CAM framework represents a groundbreaking paradigm shift in the micromechanics of composites, redefining the very philosophy that underpins our understanding of their behavior at the microscopic level.

physics.class-ph↗

arXiv2025

Additive general integral equations in thermoelastic micromechanics of composites

This work presents an enhanced Computational Analytical Micromechanics (CAM) framework for the analysis of linear thermoelastic composite materials (CMs) with random microstructure. The proposed approach is grounded in an exact Additive General Integral Equation (AGIE), specifically formulated for compactly supported loading, including both body forces and localized thermal changes (such as those from laser heating). New general integral equations (GIEs) for arbitrary mechanical and thermal loading are proposed. A unified iterative solution strategy is developed for the static AGIE, applicable to CMs with both perfectly and imperfectly bonded interfaces, where the compact support of loading is introduced as a new fundamental training parameter. Central to this methodology is a generalized Representative Volume Element (RVE) concept, which extends Hill classical definition. The resulting RVE is not predefined geometrically, but rather emerges from the characteristic scale of the localized loading, effectively reducing the analysis of an infinite, randomly heterogeneous medium to a finite, data-driven domain. This generalized RVE approach enables automatic exclusion of unrepresentative subsets of effective parameters, while inherently eliminating boundary effects, edge artifacts, and finite size limitations. Moreover, the AGIE-based CAM framework is naturally compatible with machine learning (ML) and neural network (NN) architectures, facilitating the construction of accurate and physically informed surrogate nonlocal operators.

physics.comp-ph↗

arXiv2024

Critical analyses of RVE concepts in local and peridynamic micromechanics of composites

A static peridynamic (proposed by Silling, see J. Mech. Phys. Solids 2000; 48:175--209) composite materials (CMs) of the random and periodic structures are considered. In the framework of the second background of micromechanics (also called computational analytical micromechanics, CAM), one proved that local micromechanics (LM) and peridynamic micromechanics (PM) are formally similar to each other for CM of both random and periodic structures. It allows for the straightforward generalization of LM methods to their PM counterparts. The representative volume element (RVE) playing a central role in the LM is generalized to PM. For the inhomogeneous body force with compact support, CAM is developed for the estimation of the effective behavior of CM which is used as a new compressed dataset. The preparation of these datasets is selected by the use of a fundamentally new RVE concept that directly depends on neither constitutive laws of phases nor the form of the predicted effective (surrogate) operator. The mentioned datasets with intrinsically incorporated new RVE concept as a necessary ingredient can be implemented into any known machine learning (ML) and neural network (NN) technique used for the prediction of nonlocal surrogate operators. Exploitation of the new RVE concept eliminates any potential incorrectness related to both size scale, boundary layer, and edge effects.

cond-mat.mtrl-sci↗

arXiv2009

On the thermo-elastostatics of heterogeneous materials. I. General integral equation

We consider a linearly thermoelastic composite medium,which consists of a homogeneous matrix containing a statistically inhomogeneous random set of inclusions, when the concentration of the inclusions is a function of the coordinates (so-called Functionally Graded Materials). The composite medium is subjected to essentially inhomogeneous loading by the fields of the stresses, temperature and body forces (e.g. for a centrifugal load). The general integral equations connecting the stress and strain fields in the point being considered and the surrounding points are obtained for the random fields of inclusions. The method is based on a centering procedure of subtraction from both sides of a known initial integral equation their statistical averages obtained without any auxiliary assumptions such as, e.g., effective field hypothesis implicitly exploited in the known centering methods. In so doing the size of a region including the inclusions acting on a separate one is finite, i.e. the locality principle takes place.

cond-mat.mtrl-sci↗

arXiv2009

On the thermo-elastostatics of heterogeneous materials. II. Analyze and generalization of some basic hypotheses

One considers linearly thermoelastic composite media, which consist of a homogeneous matrix containing a statistically homogeneous random set of ellipsoidal uncoated or coated inclusions. Effective properties (such as compliance and thermal expansion) as well as the first statistical moments of stresses in the phases are estimated for the general case of nonhomogeneity of the thermoelastic inclusion properties. At first, one shortly reproduces both the basic assumptions and propositions of micromechanics used in most popular methods, namely: effective field hypothesis, quasi-crystallite approximation, and the hypothesis of "ellipsoidal symmetry". The explicit new representations of the effective thermoelastic properties and stress concentration factor are expressed through some building blocks described by numerical solutions for both the one and two inclusions inside the infinite medium subjected to both the homogeneous and inhomogeneous remote loading. The method uses as a background the new general integral equation proposed in the accompanied paper and makes it possible to abandon the basic concepts of micromechanics mentioned above. The results of this abandonment are quantitatively estimated for some modeled composite reinforced by aligned continously inhomogeneous fibers. Some new effects are detected that are impossible in the framework of a classical background of micromechanics.

cond-mat.mtrl-sci↗

arXiv2009

On some background of micromechanics of random structure matrix composites

We consider a linearly elastic composite medium, which consists of a homogeneous matrix containing statistically inhomogeneous random set of heterogeneities and loaded by inhomogeneous remote loading. The new general integral equation is obtained by a centering procedure without any auxiliary assumptions such as, e.g., effective field hypothesis implicitly exploited in the known centering methods. The method makes it possible to abandon the basic concepts of classical micromechanics such as effective field hypothesis, and the hypothesis of "ellipsoidal symmetry". The results of this abandonment leads to detection of some fundamentally new effects that is impossible in the framework of a classical background of micromechanics.

cond-mat.mtrl-sci↗