On the choice of boundary conditions in problems of the local gradient approach in thermomechanics

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.

Section: Inductionmentioning

confidence: 99%

Section: Quasi-static and Stationary Statesmentioning

confidence: 99%

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

Bozhenko¹,

Nahirnyj²,

Tchervinka³

2016

“…The technique involving the application of mass sources for modeling surface roughness is proposed in [3][4][5]. In works [6,7] the key systems of equations of the mathematical model of a locally inhomogeneous electrically conductive non-ferromagnetic solid with consideration of the size effect were formulated, and the corresponding boundary conditions for the mass density distribution were substantiated in [8,9]. Since all mechanical properties (density, elasticity, and others) are determined by the state of the spatial structure of the material of the body [10], a natural extension of the model is to take into account the heterogeneity of the modulus of elasticity [2].…”

Section: Introductionmentioning

confidence: 99%

Stress-deformed state and strength of a locally heterogeneous electrically conductive layer

Markovych¹,

Senyk²,

Nodzhak³

2022

The key system of equations of the solid body model is presented, taking into account the structural heterogeneity of the material and the roughness of the real surface, which is applied to the study of interconnected fields in an unbounded heterogeneous conductive layer. The effect of taking into account the dependences on the density of local Young's modulus and Poisson's ratio on the size effects of surface stresses in the layer and its strength limit is considered.

“…However, further studies have shown that there are no methods for direct determination of the chemical potential. In [16], Nahirnyj et al have introduced a new interpretation of the local gradient approach proposing a formulation of the boundary conditions for density based on non-homogeneity of the surface geometry (surface roughness).…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of near-surface non-homogeneity in nanoelements

Nahirnyj¹,

Tchervinka²

2014

This paper is a further development of the local gradient approach in thermomechanics. The presented model allows us to study the stress-strain state of nanoelements under one-continuum approach. Thermoelastic body is considered as an open thermodynamical system where the mass fluxes and sources are connected with sudden occurrence of the structure of material and real surface of the body at the moment of body formation. The complete system of equations includes mass balance equation generalized for locally heterogeneous systems. As a model problem, there is considered an equilibrium state of a thin layer (film). The size effects of near-surface stress and effective Young's modulus have been studied.