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On nonlocal modeling in continuum mechanics

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Treść / Zawartość
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Warianty tytułu
PL
Modelowanie nielokalne w mechanice kontinuum
Języki publikacji
EN
Abstrakty
EN
The objective of the paper is to provide an overview of nonlocal formulations for models of elastic solids. The author presents the physical foundations for nonlocal theońes of continuum mechanics, followed by vanous analytical and numeńcal techniques. The characteristics and range of practical applications for the presented approaches are discussed. The results of numerical simulations for the selected case studies are provided to demonstrate the properties of the described methods. The paper is illustrated with outcomes from peridynamic analyses. Fatigue and axial stretching were simulated to show the capabilities of the developed numeńcal tools.
PL
W artykule dokonano przeglądu nielokalnych sformułowań dla mechaniki bryły odkształcalnej. Autor przedstawia podstawy fizyczne nielokalnych teorii mechaniki kontinuum oraz dokonuje przeglądu technik analitycznych i numerycznych stosowanych w modelach matematycznych. W pracy przedyskutowano charakterystyki oraz zakres praktycznych zastosowań wspomnianych technik modelowania. Ocena własności nielokalnych modeli została przeprowadzana na podstawie wyników symulacji numerycznych dla wybranych typów analiz z zastosowaniem perydynamiki. Przedstawiono wyniki symulacji zmęczeniowych oraz jednoosiowego rozciągania, uzyskane przy użyciu opracowanych narzędzi analiz symulacyjnych.
Rocznik
Strony
41--46
Opis fizyczny
Bibliogr. 43 poz., rys.
Twórcy
autor
  • AGH University of Science and Technology, Faculty of Mechanical Engineering and Robotics, Department of Robotics and Mechatronics, Krakow, Poland
Bibliografia
  • 1. Aksoylu B., Parks M.L., 2011, Variational theory and domain decomposition for nonlocal problems. Applied Mathematics and Computation 217, 6498-6515.
  • 2. Arash B., Wang Q., Liew K.M., 2012, Wave propagation in graphene sheets with nonlocal elastic theory via finite element formulation. Computer Methods Applied Mechanics and Engineering 223-224,1-9.
  • 3. Badnava H., Kadkhodaei M., Mashayekhi M., 2014,^4 non-local implicit gradient-enhanced model for unstable behaviors of pseudoelastic shape memory alloys in tensile loading. International lournal of Solids and Structures 51(23-24), 4015-4025.
  • 4. Balta E, Suhubi E.S., 1977, Theory of nonlocal generalised thermoelasti-city. International lournal of Engineering Science 15(9-10), 579-588.
  • 5. Bażant Z.P., lirasek M., 2002, Nonlocal integral formulations of plasticity and damage: survey of progress. lournal of Engineering Mechanics 128(11), 1119-1149.
  • 6. Bobaru E, Yang M., Alves L.F., Silling S.A., Askari E., Xu I., 2009, Convergence, adaptive refinement, and scaling in ID peridyna-mics. International lournal for Numerical Methods in Engineering 77, 852-877.
  • 7. Chang D.M., Wang B.L., 2015, Surface thermal shock cracking of a semi-infinite medium: a nonlocal analysis. Acta Mechanica 226, 4139^147.
  • 8. Chen Y., Lee J.D., Eskandarian A., 2004, Atomistic viewpoint of the applicability of microcontinuum theories. International Journal of Solids and Structures 41, 2085-2097.
  • 9. Di Paola M., Pirrotta A., Zingales M., 2010, Mechanically-based approach to non-local elasticity: Variationalprinciples. International Journal of Solids and Structures 47, 539-548.
  • 10. Duruk N., Erbay H.A., Erkip A., 2010, Global existence and blow-up for a class of nonlocal nonlinear Cauchy problems arising in elasticity. Nonlinearity 23, 107-118.
  • 11. Duval A., Haboussi M., Zineb T.B., 2010, Modeling of SMA superela-stic behavior with nonlocal approach. Physics Procedia 10, 33-38.
  • 12. Eringen A.C., 1972, Linear theory of nonlocal elasticity and dispersion plane waves. International Journal of Engineering Science 10, 425-435.
  • 13. Eringen AC, 1974, Theory of nonlocal thermoelasticity. International Journal of Engineering Science 12(12), 1063-1077.
  • 14. Eringen A.C., 1984, Theory of nonlocal piezoelectricity. Journal of Mathematical Physics 25(3), 717-727.
  • 15. Eringen A.C., 1992, Vistas of nonlocal continuum physics. International Journal of Engineering Science 30(10), 1551- 1565.
  • 16. Eringen A.C., Edelen D.G.B., 1972, On nonlocal elasticity. International Journal of Engineering Science 10, 233-248.
  • 17. Fornberg B., 1998, Calculation of weights in finite difference formulas. SIAM Review 40(3), 685-691.
  • 18. Ghrist M.L., 2000, High-order finite difference methods for wave equations. PhD thesis, University of Colorado.
  • 19. Gunzburger M., Lehoucq R.B., 2010, A nonlocal vector calculus with application to nonlocal boundary value problems. Multiscale Modeling and Simulation 8(5), 1581-1598.
  • 20. Haque A., Ali M., 2005, High strain rate responses and failure analysis in polymer matrix composites - an experimental and finite element study. Journal of Composite Materials 39, 423-450.
  • 21. Hu W., Ha Y.D., Bobaru E, 2012, Peridynamic model for dynamic fracture in unidirectional fiber-reinforced composites. Computer Methods in Applied Mechanics and Engineering 217-220, 247-261.
  • 22. Kaliski S., Rymarz C, Sobczyk K., Włodarczyk E., 1992, Vibrations and waves, Part B: Waves. Studies in Applied Mechanics 30B, Elsevier, Amsterdam - London - New York - Tokyo, PWN -Polish Scientific Publishers, Warsaw.
  • 23. Kroner E., 1967, Elasticity theory of materials with long range cohesive forces. International Journal of Solids and Structures 3(5), 731-742.
  • 24. Kunin I.A., 1967, Inhomogeneous elastic medium with non-local interactions. Journal of Applied Mechanics and Technical Physics 8(3), 60-66.
  • 25. Kunin I.A., 1983, Elastic media with micro structure II: Three-dimensional models. Springer-Verlag, Berlin - Heidelberg.
  • 26. Leamy M.J., Springer AC, 2011, Parallel implementation of triangular cellular automata for computing two-dimensional elasto-dynamic response on arbitrary domains. Vibration Problems ICOVP 2011. The 10th International Conference on Vibration Problems, Naprstek J., Horacek J., Okrouhlik M., Marvalova B., Verhulst E, Sawicki J.T (eds.), Springer Proceedings in Physics 139, 731-736.
  • 27. Madenci E., Oterkus E., 2014, Peridynamic theory and its applications. Springer, New York.
  • 28. Martowicz A., Ruzzene M., Staszewski W.J., Rimoli J.J., Uhl T, 2014a, A nonlocal finite difference scheme for simulation of wave propagation in 2D models with reduced numerical dispersion. Proceedings of SPIE 9064, Health Monitoring of Structural and Biological Systems 2014, Article ID 90640F, doi: 10.1117/12.2045252.
  • 29. Martowicz A, Ruzzene M., Staszewski W.J., Uhl T, 2014b, Non-local modeling and simulation of wave propagation and crack growth. AIP Conference Proceedings 1581, 513, AIP Publishing.
  • 30. Martowicz A., Staszewski W.J., Ruzzene M., Uhl T, 2014c, Vibro--acoustic wave interaction in cracked plate modeled with peridyna-mics. A Proceedings of the WCCM XI, ECCM V, ECFD VI, Onate E., Oliver X., Huerta (eds.), International Center for Numerical Methods in Engineering, Barcelona, Spain, 4021^1027.
  • 31. Martowicz A., Ruzzene M., Staszewski W.J., Rimoli J.J., Uhl T, 2015a, Out-of-plane elastic waves in 2D models of solids: A case study for a nonlocal discretization scheme with reduced numerical dispersion. Mathematical Problems in Engineering 2015, Article ID 584081.
  • 32. Martowicz A., Staszewski W.J., Ruzzene M., Uhl T, 2015b, Peridyna-mics as an analysis tool for wave propaga tion in graphene nanorib-bons. Proceedings of SPIE, Volume 9435: Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems, Lynch J.P. (ed.), San Diego, USA, Article ID 943501, doi: 10.1117/12.2084312.
  • 33. Meyers M., Chawla K., 2009, Mechanical behaviour of materials. Cambridge University Press, Cambridge.
  • 34. Ostoja-Starzewski M., 2013, From random fields to classical or generalized continuum models. Procedia IUTAM 6, 31-34.
  • 35. Polizzotto C, 2001, Nonlocal elasticity and related variational principles. International Journal of Solids and Structures 38, 7359-7380.
  • 36. Rodriguez-Ferran A., Morata I., Huerta A., 2004, Efficient and reliable nonlocal damage models. Computer Methods in Applied Mechanics and Engineering 193, 3431-3455.
  • 37. Seleson P., Parks M.L., Gunzburger M., Lehoucq R.B., 2009, Peridyna-mics as an upscaling of molecular dynamics. Multiscale Modeling and Simulation 8(1), 204-227.
  • 38. Sguazzero P., Kindelan M., 1990, Dispersion-bounded numerical integration of the elastodynamic equations with cost-effective staggered schemes. Computer Methods in Applied Mechanics and Engineering 80(1-3), 165-172.
  • 39. Silling S., 2000, Reformulation of elasticity theory for discontinuities and long-range forces. Journal of Mechanics Physics of Solids 48, 175-209.
  • 40. Tam C.K.W, Webb J.C, 2011, Dispersion-relation-preserving finite difference schemes for computational acoustics. Journal of Computations Physics 107(2), 262-281.
  • 41. Yang D., Tong P., Deng X., 2012, A central difference method with low numerical dispersion for solving the scalar wave equation. Geophysical Prospecting 60, 885-905.
  • 42. Zhang L.L., Liu J.X., Fang X.Q., Nie G.Q., 2014, Effects of surface piezoelectricity and nonlocal scale on wave propagation in piezoelectric nanoplates. European Journal of Mechanics - A/Solids 46,22-29.
  • 43. Zingales M., 2011, Wave propagation in ID elastic solids in presence of long-range. Journal of Sound and Vibration 330, 3973-3989.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a97d38ae-4219-4f05-82fe-c6aad3bd801d
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