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Modelling and numerical treatment of scale effects in nanoscopic structures
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DOI：10.1016/j.mechrescom.2026.104653.png)
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Abstract
En 中文
In this paper, we discuss physical aspects, which appear to be inevitable for explanation of size-effects in nanoscopic structures described within continuum theories. Three continuum models are compared in order to indicate the role of scale dependence of dimensionless formulation of a continuum model for phenomenological explanation of size-effects. The attention is paid to treatment of continuity of approximation of primary field variables in weak formulations of governing equations within higher-grade continuum theory, because of higher order derivatives in the governing equations. The importance of modelling real dimensionality in higher-grade continuum theory is demonstrated in an illustrative example. The heat conduction is studied within the higher-grade continuum theory for a simple 1D problem in an infinite bilayer. The boundary conditions considered on the material interface reflect either perfect contact or the interface thermal resistance phenomenon. The variety of boundary conditions together with material parametric study allow to draw conclusions concerning formulation of necessary conditions for occurrence higher-grade theory effects (including size-effects), which are not observable in the classical theory.
Keywords:
Higher-order gradients
Nonlocal theories
Size-effects
Moving FEM
Mixed FEM
Non-Fourier heat conduction
Journal
M
IF:
2.3
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115
Citations:
3.9K
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