Near-surface mass defect in models of locally heterogeneous solid mechanics

• Autorzy: Nahirnyj Taras , Tchervinka Kostiantyn

Identyfikatory

DOI

10.2478/ama-2019-0027

• Języki publikacji: EN

Abstrakty

EN

This article deals with the model of the locally heterogeneous elastic body. The model accounts for long-range interaction and describes near-surface non-homogeneity and related size effects. The key systems of model equations are presented. From the viewpoint of the representative volume element, the boundary condition for density and the limits of applicability of the model are discussed. The difference of mass density in the near-surface body region from the reference value (near-surface mass defect) causes a non-zero stressed state. It is indicated on the strong dependence of the surface value of density from the curvature of the surface of thin fibres. The effect of the near-surface mass defect on the stressed state and the size effect of surface stresses have been investigated on an example of a hollow cylinder. Size effect of its strength has been studied as well.

Słowa kluczowe

EN

locally heterogeneous mechanics; RVE; mass defect; size effects; thin fibres

• Wydawca: Oficyna Wydawnicza Politechniki Białostockiej
• Czasopismo: Acta Mechanica et Automatica
• Rocznik: 2019
• Tom: Vol. 13, no. 3
• Strony: 205--210
• Opis fizyczny: Bibliogr.30 poz., rys., wykr.

Twórcy

autor

Nahirnyj Taras

• *Faculty of Mechanical Engineering, Institute of Computer Science and Production Management, University of Zielona Góra, ul. prof. Z. Szafrana 4, 65-516 Zielona Góra, Poland

autor

Tchervinka Kostiantyn

• Mathematical Modeling Department, Mechanical and Mathematical Faculty, Ivan Franko University of Lviv, 1 Universytetska str., Ukraine 79000 Lviv, Ukraine
• Centre of Mathematical Modeling of Ukrainian National Academy of Sciences, 15 Dudaeva Str., Ukraine 70005, Lviv, Ukraine

Bibliografia

• 1. Aifantis E. C. (2011), On the gradient approach-relation to Eringen’s nonlocal theory, International Journal of Engineering Science, 49(12), 1367–1377.
• 2. Bargmann S., Klusemann B., Markmann J., Schnabel J. E., Schneider K., Soyarslan C., Wilmers J. (2018), Generation of 3D representative volume elements for heterogeneous materials: A review,Progress in Materials Science, 96, 322-384.
• 3. Bažant Z. P., Jirásek M. (2002), Nonlocal integral formulations of plasticity and damage: Survey of progress,Journal of Engineering Mechanics, 128(11),1119–1149.
• 4. Bostanabad R., Zhang Y., Li X., Kearney T., Brinson L., Apley D., Liu W., Chen W. (2018), Computational microstructure characterization and reconstruction: Review of the state-of-the-art techniques,Progress in Materials Science, 95, 1-41.
• 5. Burak Y., Nahirnyj T., Tchervinka K. (2014), Local gradient thermomechanics, Encyclopedia of Thermal Stresses, 2794–2801.
• 6. Cheng A. H-D. (2016), Poroelasticity, Vol. 27, Springer.
• 7. Di Paola M., Failla, G., Zingales M. (2010), The mechanically-based approach to 3D non-local linear elasticity theory: Long-range central interactions, International Journal of Solids and Structures, 47(18- 19), 2347-2358.
• 8. Dormieux L., Kondo D. (2013), Non linear homogenization approach of strength of nanoporous materials with interface effects, International Journal of Engineering Science, 71, 102–110.
• 9. Dormieux L., Kondo D., Ulm F.-J. (2006), Microporomechanics, John Wiley and Sons.
• 10. Drugan W.J., Willis J.R. (1996), A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites, Journal of the Mechanics and Physics of Solids, 44(4), 497–524.
• 11. Eringen A. C. (2002), Nonlocal continuum field theories. Springer.
• 12. Guo N., Zhao J. (2016), 3D multiscale modeling of strain localization in granular media, Computers and Geotechnics, 80, 360-372.
• 13. Kanit T., Forest S., Galliet I., Mounoury V., Jeulin, D. (2003), Determination of the size of the representative volume element for random composites: statistical and numerical approach,International Journal of Solids and Structures, 40(13-14), 3647–3679.
• 14. Karlicic D., Murmu T., Adhikari S., McCarthy M. (2015), Non-local structural mechanics. John Wiley and Sons.
• 15. Khodabakhshi P., Reddy J. N. (2015), A unified integro-differential nonlocal model, International Journal of Engineering Science, 95, 60-75.
• 16. Kwok K., Boccaccini D., Persson Å. H., Frandsen H. L. (2016). Homogenization of steady-state creep of porous metals using threedimensional microstructural reconstructions, International Journal of Solids and Structures, 78, 38-46.
• 17. Marotti de Sciarra F. (2009), On non-local and non-homogeneous elastic continua, International Journal of Solids and Structures, 46(3), 651–676.
• 18. Matouš K., Geers M. G., Kouznetsova V. G., Gillman A. (2017), A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials, Journal of Computational Physics, 330, 192-220.
• 19. Monetto I., Drugan W. J. (2009), A micromechanics-based nonlocal constitutive equation and minimum RVE size estimates for random elastic composites containing aligned spheroidal heterogeneities,Journal of the Mechanics and Physics of Solids, 57(9), 1578-1595.
• 20. Nahirnyj T., Tchervinka K. (2015), Mathematical Modeling of Structural and Near-Surface Non-Homogeneities in Thermoelastic Thin Films,International Journal of Engineering Science, 91, 49–62.
• 21. Nahirnyj T., Tchervinka K. (2018), Fundamentals of the mechanics of locally non-homogeneous deformable solids, Lviv: Rastr-7 (in ukr).
• 22. Polizzotto C. (2003), Gradient elasticity and nonstandard boundary conditions, International Journal of Solids and Structures, 40(26), 7399–7423.
• 23. Polizzotto C. (2012), A gradient elasticity theory for second-grade materials and higher order inertia, International Journal of Solids and Structures, 49 (15), 2121–2137.
• 24. Rezakhani R., Zhou X.W., Cusatis G. (2017), Adaptive multiscale homogenization of the lattice discrete particle model for the analysis of damage and fracture in concrete, International Journal of Solids and Structures, 2017, 125, 50-67.
• 25. Saeb S., Steinmann P., Javili A. (2016), Aspects of computational homogenization at finite deformations: a unifying review from Reuss' to Voigt's bound, Applied Mechanics Reviews, 68(5), 050801.
• 26. Salmi M., Auslender F., Bornert M., Fogli M. (2012), Various estimates of Representative Volume Element sizes based on a statistical analysis of the apparent behavior of random linear composites,Comptes Rendus Mécanique, 340(4-5), 230-246.
• 27. Silling S.A. (2000), Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces. Journal of the Mechanics and Physics of Solids, 48, 175–209.
• 28. Sneddon I.N., Berry D.S. (1958), The Classical Theory of Elasticity. In: Flügge S. (eds) Elasticity and Plasticity / Elastizität und Plastizität. Handbuch der Physik / Encyclopedia of Physics, 3/6, Springer, Berlin, Heidelberg.
• 29. Wang Q., Liew K. (2007), Application of nonlocal continuum mechanics to static analysis of micro- and nano-structures, Physics Letters A, 363(3), 236–242.
• 30. Wiśniewska A., Hernik S., Liber-Kneć A., Egner H. (2019), Effective properties of composite material based on total strain energy equivalence, Composites Part B: Engineering, 166, 213-220.