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Mathematical Modeling of the Coupled Processes in Nanoporous Bodies Cover

Mathematical Modeling of the Coupled Processes in Nanoporous Bodies

Open Access
|Oct 2018

References

  1. 1. Abeyaratne R., Knowles J.K. (1991), Kinetic relations and the propagation of phase boundaries in solids, Archive for Rational Mechanics and Analysis, 114(2), 119–154.10.1007/BF00375400
  2. 2. Aifantis E.C. (2011b), On the gradient approach–relation to Eringen’s nonlocal theory, International Journal of Engineering Science, 49(12), 1367–1377.10.1016/j.ijengsci.2011.03.016
  3. 3. Aifantis E.C. (2011a), Gradient nanomechanics: applications to deformation, fracture, and diffusion in nanopolycrystals, Metallurgical and Materials Transactions A, 42(10), 2985.10.1007/s11661-011-0725-9
  4. 4. Bao Y., Wen T., Samia A.C.S., Khandhar A., Krishnan K.M. (2016), Magnetic nanoparticles: material engineering and emerging applications in lithography and biomedicine, Journal of Materials Science, 51(1), 513–553.10.1007/s10853-015-9324-2
  5. 5. Berezovski A., Engelbrecht J., Maugin G.A. (2007), Front dynamics in inhomogeneous solids. Proc. Estonian Acad. Sci. Phys. Math., 56(2), 155–161.10.3176/phys.math.2007.2.11
  6. 6. Bhattacharya A., Calmidi V.V., Mahajan R.L. (2002), Thermo-physical properties of high porosity metal foams, International Journal of Heat and Mass Transfer, 45(5), 1017–1031.10.1016/S0017-9310(01)00220-4
  7. 7. Biot M.A. (1941), General theory of three dimensional consolidation, Journal of Applied Physics, 12, 155–164.10.1063/1.1712886
  8. 8. Bozhenko B., Nahirnyj T., Tchervinka K. (2016), To modeling admixtures influence on the size effects in a thin film, Mathematical Modeling and Computing, 3(1), 12–22.10.23939/mmc2016.01.012
  9. 9. Burak Y.I., Nagirnyi T. (1992), Mathematical modeling of local gradient processes in inertial thermomechanical systems, International applied mechanics 28(12), 775–793.10.1007/BF00847314
  10. 10. Charalambakis N. (2010), Homogenization techniques and micro-mechanics. A survey and perspectives, Applied Mechanics Reviews, 63(3), 030803.10.1115/1.4001911
  11. 11. Coussy O. (2004), Poromechanics, John Wiley & Sons.10.1002/0470092718
  12. 12. Dönmez A., Bažant Z.P. (2017), Size effect on punching strength of reinforced concrete slabs with and without shear reinforcement, ACI Structural Journal, 114(4), 875.10.14359/51689719
  13. 13. Elliott J.A. (2011), Novel approaches to multiscale modelling in materials science, International Materials Reviews, 56(4), 207–225.10.1179/1743280410Y.0000000002
  14. 14. Eringen A.C. (2002), Nonlocal continuum field theories, Springer Science & Business Media.
  15. 15. Eringen A.C., Edelen D.G.B. (1972), On nonlocal elasticity, International Journal of Engineering Science, 10(3), 233–248.10.1016/0020-7225(72)90039-0
  16. 16. Geers M.G., Kouznetsova V., Brekelmans W.M. (2002), Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme, International Journal for Numerical Methods in Engineering, 54(8), 1235–1260.10.1002/nme.541
  17. 17. Geers M.G.D., De Borst R., Peerlings R.H.J., Brekelmans W.A.M. (2001), A critical comparison of nonlocal and gradient-enhanced softening continua, International Journal of Solids and Structures, 38(44), 7723–7746.10.1016/S0020-7683(01)00087-7
  18. 18. Hu H., Onyebueke L., Abatan A. (2010), Characterizing and modeling mechanical properties of nanocomposites-review and evaluation, Journal of Minerals and Materials Characterization and Engineering, 9(04), 275.10.4236/jmmce.2010.94022
  19. 19. Kachanov M., Sevostianov I. (2018), Quantitative Characterization of Microstructures in the Context of Effective Properties, In Micromechanics of Materials, with Applications (pp. 89–126), Springer, Cham.10.1007/978-3-319-76204-3_2
  20. 20. Kalamkarov A.L., Andrianov I.V., Danishevsâ V.V. (2009), Asymptotic homogenization of composite materials and structures, Applied Mechanics Reviews, 62(3), 030802.10.1115/1.3090830
  21. 21. Markov K.Z. (2000), Elementary micromechanics of heterogeneous media, In Heterogeneous Media (pp. 1–162), Birkhäuser, Boston, MA.10.1007/978-1-4612-1332-1_1
  22. 22. Maugin G.A. (1979), Nonlocal theories or gradient-type theories-a matter of convenience, Archiv of Mechanics, Archiwum Mechaniki Stosowanej, 31, 15–26.
  23. 23. Nahirnyj T., Tchervinka K. (2012), Thermodynamical models and methods of thermomechanics taking into account nearsurface and structural nonhomogeneity. Bases of nanomechanics I, Spolom, Lviv (In Ukrainian).
  24. 24. Nahirnyj T., Tchervinka K. (2013), Structural inhomogeneity and size effects in thermoelastic solids, J. Coupled Syst. Multiscale Dyn., 1, 216–223.10.1166/jcsmd.2013.1015
  25. 25. Nahirnyj T., Tchervinka K. (2014), Basics of mechanics of local non-homogeneous elastic bodies. Bases of nanomechanics II, Rastr-7, Lviv (In Ukrainian).
  26. 26. Nahirnyj T., Tchervinka K. (2015), Mathematical Modeling of Structural and Near-Surface Non-Homogeneities in Thermoelastic Thin Films, International Journal of Engineering Science, 91, 49–62.10.1016/j.ijengsci.2015.02.001
  27. 27. Pindera M.J., Khatam H., Drago A.S., Bansal Y. (2009), Microme-chanics of spatially uniform heterogeneous media: a critical review and emerging approaches, Composites Part B: Engineering, 40(5), 349–378.10.1016/j.compositesb.2009.03.007
  28. 28. Polizzotto C. (2003), Unified thermodynamic framework for nonlocal / gradient continuum theories, European Journal of Mechanics-A / Solids, 22(5), 651–668.10.1016/S0997-7538(03)00075-5
  29. 29. Rabotnov Yu.N. (1980), Elements of Hereditary Solid Mechanics, Mir Publ. Moscow (in Russian).
  30. 30. Rafii-Tabar H., Ghavanloo E., Fazelzadeh S.A. (2016), Nonlocal continuum-based modeling of mechanical characteristics of nanoscopic structures, Physics Reports, 638, 1–97.10.1016/j.physrep.2016.05.003
  31. 31. Rosakis P., Knowles J.K. (1997), Unstable kinetic relations and the dynamics of solid-solid phase transitions, Journal of the Mechanics and Physics of Solids, 45(11), 2055–2081.10.1016/S0022-5096(97)00026-4
  32. 32. Tappan B.C., Steiner S.A., Luther E.P. (2010), Nanoporous metal foams, Angewandte Chemie International Edition, 49(27), 4544–4565.10.1002/anie.200902994
  33. 33. Vafai K. (2015), Handbook of porous media, Crc Press.10.1201/b18614
  34. 34. Wang Y.M., Ma E. (2009), Mechanical properties of bulk nanostructured metals, Bulk Nanostructured Materials, 423–453.10.1002/9783527626892.ch19
  35. 35. Woźniak C. (1987), A nonstandard method of modelling of thermo-elastic periodic composites, International Journal of Engineering Science, 25(5), 483-498.10.1016/0020-7225(87)90102-9
  36. 36. Young R., Kinloch I.A., Gong L., Novoselov K.S. (2012), The mechanics of graphene nanocomposites: a review, Composites Science and Technology, 72(12), 1459–1476.10.1016/j.compscitech.2012.05.005
DOI: https://doi.org/10.2478/ama-2018-0030 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088
Language: English
Page range: 196 - 203
Submitted on: Apr 5, 2017
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Accepted on: Aug 27, 2018
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Published on: Oct 16, 2018
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2018 Taras Nahirnyj, Kostiantyn Tchervinka, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.