Error message

  • Deprecated function: Unparenthesized `a ? b : c ? d : e` is deprecated. Use either `(a ? b : c) ? d : e` or `a ? b : (c ? d : e)` in include_once() (line 1439 of /home/science2016/public_html/includes/bootstrap.inc).
  • Deprecated function: Array and string offset access syntax with curly braces is deprecated in include_once() (line 3557 of /home/science2016/public_html/includes/bootstrap.inc).

Mathematical modeling of near-surface non-homogeneity in nanoelements

Nahirnyj T. S., Tchervinka K. A.
AttachmentSize
PDF icon 2014_1_061_074.pdf1.25 MB

Keywords:

Abstract: 
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.
References: 
  1. Aifantis E. Exploring the applicability of gradient elasticity to certain micro/nano reliability problems. Microsyst. Technol. 15, 109 (2009).
  2. Aliofkhazraei M. Nanocoatings: Size Effect in Nanostructured Films. Springer-Verlag Berlin Heidelberg (2011).
  3. Bažant Z. P. Scaling of Structural Strength Elsevier Butterworth-Heinemann Linacre House, Jordan Hill, Oxford, Burlington, MA (2005).
  4. Burak Y. I., Nagirnyi T. S. Mathematical modeling of local gradient processes in inertial thermomechanical systems. Int. Appl. Mech. 28, 775 (1992).
  5. Burak Y. Nahirnyj T., Tchervinka K. Local Gradient Thermomechanics. In: Richard B. Hetnarski (eds). Encyclopedia of Thermal Stresses, Springer Reference: 2794–2801 (2014).
  6. Cuenot S., Frétigny C., Demoustier-Champagne S., Nysten B. Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy. Phys. Rev. B 69, 16, 165410–165415 (2004).
  7. Eringen C. Nonlocal continuum field theories. Springer-Verlag New York (2002).
  8. Ghoniem N. M., Busso E. P., Kioussis N., Huang H. Multiscale modelling of nanomechanics and micromechanics: An overview. Phil. Mag. 8331, 3475 (2003).
  9. Glansdorff P., Prigogine I. Thermodynamic Theory of Structure, Stability and Fluctuations. Wiley, New York (1971).
  10. Kim T.-Y., Dolbow J. E., Fried E. Numerical study of the grain-size dependent Young’s modulus and Poisson’s ratio of bulk nanocrystalline materials. Int. J. Solid Struct. 49, 3942 (2012).
  11. Kröner E. Elasticity theory of materials with long range cohesive forces. Int. J. Solid. Struct. 3, 731–742 (1967).
  12. Liang H., Upmanyu M., Huang H. Size-dependent elasticity of nanowires: Nonlinear effects. Phys. Rev. B 71, 241403(R) (2005).
  13. Lykov A. V. Teoriya teploprovodnosti [Theory of thermal conductivity]. Moscow: Visshaya shkola (1967).
  14. Manoharan M. P., Lee H., Rajagopalan R., Foley H. C., Haque M. A. Elastic properties of 4–6 nm-thick glassy carbon thin films. Nanoscale Res. Lett. 5:14–19 (2010).
  15. Maugin G. A. Nonlocal theories or gradient-type theories – A matter of convenience. Arch. Mech. 31, 15 (1979).
  16. Nahirnyj T. S., Chervinka K. A., Boiko Z. V. On the choice of boundary conditions in problems of the local gradient approach inthermomechanics. J. Math. Sci. 186, 130 (2012).
  17. Nahirnyj T., Tchervinka K. Surface tension and strength of local nonhomogeneous cylinder in the process of heating. Phys.-Math. Model. Inf. Tech. 7, 30 (2008).
  18. Nahirnyj T., Tchervinka K. Thermodynamical models and methods of thermomechanics taking into account near-surface and structural nonhomogeneity. Bases of nanomechanics I. Lviv, SPOLOM, (in ukrainian) (2012).
  19. Nahirnyj T., Tchervinka K. Interface phenomena and interactionenergy at the surface of electroconductive solids. Comput. Meth. Sci. Technol. 14, 105 (2008).
  20. Nowacki W. Thermoelasticity Pergamon Press Ltd, Oxford (1986).
  21. Paola M. D., Failla G., Zingales M. The mechanically-based approach to 3D non-local linear elasticity theory: Long-range central interactions. Int. J. Solid Struct. 47, 2347 (2010).
  22. Phan-Thien N. Understanding Viscoelasticity: Basics of Rheology. Springer-Verlag Berlin Heidelberg (2002).
  23. Polizzotto C. Gradient elasticity and nonstandard boundary conditions. Int. J. Solid. Struct. 40, 7399 (2003).
  24. Sciarra F. M. On non-local and non-homogeneous elastic continua. Int. J. Solid Struct. 46, 651 (2009).
  25. Schmauder S., Mishnaevsky L. Micromechanics and Nanosimulation of Metals and Composites: Advanced Methods and Theoretical Concepts. Springer-Verlag, Berlin, Heidelberg (2009).
  26. Ursenbach C. P. Simulation of elastic moduli for porous materials. CREWES Research Report. 13, 83 (2001).
  27. Vishnu K., Strachan A. Size effects in NiTi from density functional theory calculations. Phys. Rev. B 85, 014114 (2012).
  28. Wang Y. M., Ma E. Mechanical Properties of Bulk Nanostructured Metals. In: Bulk Nanostructured Materials, edited by M. J. Zehetbauer and Y. T. Zhu, Wiley-VCH, Verlag GmbH & Co., KGaA, Weinheim, pp. 425–450 (2009).
  29. Wang Z. M. Nanoporous Materials. In: Sattler K. D. (eds). Handbook of Nanophysics. Principles and Methods, CRC Press: 9-1–12 (2010).
Bibliography: 
Math. Model. Comput. Vol.1, No.1, pp.61-74 (2014)