Mathematical modeling of structural and near-surface non-homogeneities in thermoelastic thin films

Nahirnyj, Taras; Tchervinka, Kostiantyn

doi:10.1016/j.ijengsci.2015.02.001

Cited by 14 publications

(13 citation statements)

References 41 publications

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“…One of effective approaches used to describe interrelated fields in the nano elements is local gradient approach in thermomechanics [6][7][8]. The approach is based on the main principles of irreversible thermodynamics and nonlinear mechanics.…”

Section: Inductionmentioning

confidence: 99%

To modeling admixtures influence on the size effects in a thin film

Bozhenko¹,

Nahirnyj²,

Tchervinka³

2016

Math. Model. Comput.

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There are formulated the key systems of equation describing structurally nonhomogeneous two-component solid solutions. As the key functions there are chosen the stress tensor (displacement vector) and the densities of admixture and skeleton. On this basis the nearsurface nonhomogeneity densities of skeleton and admixture, stresses and size effects of surface tension and intensity of the power load causing the thin film fracture are studied. The attention is paid to the admixture influence on size effects.

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Section: Inductionmentioning

confidence: 99%

To modeling admixtures influence on the size effects in a thin film

Bozhenko¹,

Nahirnyj²,

Tchervinka³

2016

Math. Model. Comput.

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“…Here u is the velocity vector, ρ and ρ * are the densities in actual and reference state respectively, d σm is the mass source related to body structure formation [4], τ is the time, µ, λ, a m , ξ are material parameters. This system is nonlinear due to expression in the brackets in the left hand side of the first equation, this expression representing the momentum of mechanical motion.…”

Section: The Key System Of Nonhomogeneous Elastic Solid and The Averamentioning

confidence: 99%

“…The advanced approaches of continuum mechanics have to be applied to build an adequate model of the element with finite size effects, surface and interface effects. Among such approaches the approaches of nonlocal theory of elasticity [1,2] as well as local gradient approach in thermomechanics [3,4] are distinguished.…”

Section: Introductionmentioning

confidence: 99%

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Wave processes in the locally nonhomogeneous solids

Nahirnyj¹,

Tchervinka²

2015

Math. Model. Comput.

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There is proposed a method of studying wave processes in locally nonhomogeneous solids with account for geometrically non-uniform surface. The method is based on the equation system of the locally nonhomogeneous elastic solid model obtained within the local gradient approach and the use of averaging operation to separate oscillatory and slowly variable over period of oscillation components of displacement and density fields. At the example of a layer there is illustrated an application of the method to study the frequencies of natural oscillations for different fixing conditions at the layer surfaces. It was established that the dependence of frequencies of natural oscillations of the layer on the characteristic sizes the nearsurface and structural nonhomogeneities in the case of the free layer surfaces is much higher comparing to the fixed surfaces case.

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“…Its name originates from introducing gradients of state parameters into the space of thermodynamic local variables (mainly chemical potential as conjugated to the density parameter) thus increasing order and scope of classical models of solid mechanics, thermomechanics, etc. Now the thermoelastic solid body is considered as an open thermodynamic system with variable density reflecting the structure of body and its surface (Nahirnyj and Tchervinka, 2015). The density incorporation into state parameter space and the formulated equation for it allow to describe structural heterogeneity of the material, as was shown by comparison with double diffusivity models that account for two distinct diffusivity paths throught grain and grain boundary (Nahirnyj and Tchervinka, 2012).…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of the Coupled Processes in Nanoporous Bodies

Nahirnyj

Tchervinka

2018

Acta Mechanica Et Automatica

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The methods of irreversible thermomechanics and functional analysis are used to formulate the mathematical model of thermoelastic solid body taking account of structural heterogeneity of the body material and geometric irregularity of its surface. The density and the chemical potential of skeleton among others are included into the state parameters space. The source of skeleton mass reconciles the actual and reference body states and may be associated with real surface forming method. The analysis of model problem solutions shows that the model is appropriate to describe coupled processes in porous and nanoporous bodies. It allows studying the size effects of strength, elastic moduli, etc. caused by near-surface non-homogeneity.

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Mathematical modeling of structural and near-surface non-homogeneities in thermoelastic thin films

Cited by 14 publications

References 41 publications

To modeling admixtures influence on the size effects in a thin film

To modeling admixtures influence on the size effects in a thin film

Wave processes in the locally nonhomogeneous solids

Mathematical Modeling of the Coupled Processes in Nanoporous Bodies

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