Statistical homogenization of particulate composites within strain gradient elasticity

This work aims to generalize the method of conditional moments (MCM), a statistical approach developed for classical elasticity, to the case of strain gradient elasticity and to evaluate the effective properties of random particulate composites within the simplified strain gradient elasticity theory...

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Vydáno v:	Acta mechanica Ročník 236; číslo 12; s. 7181 - 7197
Hlavní autoři:	Nazarenko, Lidiia, Altenbach, Holm
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Vienna Springer Vienna 01.12.2025 Springer Nature B.V
Témata:	Classical and Continuum Physics Control Differential equations Dynamical Systems Elasticity Engineering Engineering Fluid Dynamics Engineering Thermodynamics Equilibrium Heat and Mass Transfer Homogenization Inhomogeneity Integral equations Methods Original Paper Particulate composites Shear modulus Solid Mechanics Strain Theoretical and Applied Mechanics Vibration
ISSN:	0001-5970, 1619-6937
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Abstract	This work aims to generalize the method of conditional moments (MCM), a statistical approach developed for classical elasticity, to the case of strain gradient elasticity and to evaluate the effective properties of random particulate composites within the simplified strain gradient elasticity theory. The problem of finding the effective constants is reduced to a system of stochastic differential equations based on the fundamental equations of linear elasticity, which are solved by the method of conditional moment functions. Closed-form expressions for the effective moduli of a composite with an isotropic matrix and randomly distributed spherical inhomogeneities are derived. The effective properties obtained within strain gradient elasticity depend not only on the properties of constituents, their volume fraction, shape, and distribution of inhomogeneities, but also on their size, which is impossible in the frame of usual classical elasticity. As a numerical example, it is considered a special case of a composite with an isotropic matrix and randomly distributed spherical inhomogeneities, where the materials of the matrix and the inhomogeneities are second gradient media. Variation of the normalized bulk and shear moduli of the particulate composite material as a function of volume fraction of inhomogeneity and as a function of inhomogeneity size is evaluated, analyzed, and compared in the context of other theoretical predictions.
AbstractList	This work aims to generalize the method of conditional moments (MCM), a statistical approach developed for classical elasticity, to the case of strain gradient elasticity and to evaluate the effective properties of random particulate composites within the simplified strain gradient elasticity theory. The problem of finding the effective constants is reduced to a system of stochastic differential equations based on the fundamental equations of linear elasticity, which are solved by the method of conditional moment functions. Closed-form expressions for the effective moduli of a composite with an isotropic matrix and randomly distributed spherical inhomogeneities are derived. The effective properties obtained within strain gradient elasticity depend not only on the properties of constituents, their volume fraction, shape, and distribution of inhomogeneities, but also on their size, which is impossible in the frame of usual classical elasticity. As a numerical example, it is considered a special case of a composite with an isotropic matrix and randomly distributed spherical inhomogeneities, where the materials of the matrix and the inhomogeneities are second gradient media. Variation of the normalized bulk and shear moduli of the particulate composite material as a function of volume fraction of inhomogeneity and as a function of inhomogeneity size is evaluated, analyzed, and compared in the context of other theoretical predictions.
Author	Altenbach, Holm Nazarenko, Lidiia
Author_xml	– sequence: 1 givenname: Lidiia orcidid: 0000-0001-7276-1413 surname: Nazarenko fullname: Nazarenko, Lidiia email: lidiia.nazarenko@ovgu.de organization: Institute of Materials, Technologies and Mechanics, Otto von Guericke University Magdeburg – sequence: 2 givenname: Holm surname: Altenbach fullname: Altenbach, Holm organization: Institute of Materials, Technologies and Mechanics, Otto von Guericke University Magdeburg
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SubjectTerms	Classical and Continuum Physics Control Differential equations Dynamical Systems Elasticity Engineering Engineering Fluid Dynamics Engineering Thermodynamics Equilibrium Heat and Mass Transfer Homogenization Inhomogeneity Integral equations Methods Original Paper Particulate composites Shear modulus Solid Mechanics Strain Theoretical and Applied Mechanics Vibration
Title	Statistical homogenization of particulate composites within strain gradient elasticity
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