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Peridynamic analysis of 2-dimensional deformation and fracture based on an improved technique of exerting traction on boundary surface

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Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For 2-dimensional problems in peridynamics, the transfer functions of boundary traction are constructed. The peridynamic motion equation introducing the boundary traction is improved and used to solve some typical 2-dimensional deformation and fracture problems, including the uniaxial tension and pure bending of plate, and fracture of a plate with the small circular hole or central crack. The acquired numerical solutions are close to the analytical solutions of elasticity and numerical solutions given by the finite element method. The results show that the improved technique of exerting traction on a boundary surface is valid for calculating the deformation and failure of solid. It provides a new method and path for the analysis of traction boundary value problems in peridynamics.
Rocznik
Strony
441--461
Opis fizyczny
Bibliogr. 29 poz., wykr.
Twórcy
autor
  • State Key Laboratory of Mechanics and Control of Mechanical Structures
  • Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, 210016, PR China
autor
  • State Key Laboratory of Mechanics and Control of Mechanical Structures
  • Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, 210016, PR China
autor
  • State Key Laboratory of Mechanics and Control of Mechanical Structures
  • Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, 210016, PR China
autor
  • State Key Laboratory of Mechanics and Control of Mechanical Structures
  • Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, 210016, PR China
Bibliografia
  • 1. S.A. Silling, Reformulation of elasticity theory for discontinuities and long-range forces, Journal of the Mechanics and Physics of Solids, 48, 175–209, 2000, doi: 10.1016/s0022-5096(99)00029-0.
  • 2. S.A. Silling, R.B. Lehoucq, Peridynamic theory of solid mechanics, Advances in Applied Mechanics, 44, 73–168, 2010, doi: 10.1016/S0065-2156(10)44002-8.
  • 3. W.H. Gerstle, Introduction to Practical Peridynamics: Computational Solid Mechanics Without Stress and Strain, vol. 1, World Scientific, Singapore, 2015, doi: 10.1142/9687.
  • 4. O. Weckner, R. Abeyaratne, The effect of long-range forces on the dynamics of a bar, Journal of the Mechanics and Physics of Solids, 53, 705–728, 2005, doi: 10.1016/j.jmps.2004.08.006.
  • 5. S.A. Silling, M. Zimmermann, R. Abeyaratne, Deformation of a peridynamic bar, Journal of Elasticity, 73, 173–190, 2003, doi: 10.1023/B:ELAS.0000029931.03844.4f.
  • 6. Z.X. Huang, Revisiting the peridynamic motion equation due to characterization of boundary conditions, Acta Mechanica Sinica, 35, 972–980, 2019, doi: 10.1007/s10409-019-00860-3.
  • 7. K. Zhou, Q. Du, Mathematical and numerical analysis of linear peridynamic models with nonlocal boundary conditions, SIAM Journal on Numerical Analysis, 48, 1759–1780, 2010, doi: 10.1137/090781267.
  • 8. S.A. Silling, E. Askari, A meshfree method based on the peridynamic model of solid mechanics, Computers & Structures, 83, 1526–1535, 2005, doi: 10.1016/j.compstruc. 2004.11.026.
  • 9. R.W. Macek, S.A. Silling, Peridynamics via finite element analysis, Finite Elements in Analysis and Design, 43, 1169–1178, 2007, doi: 10.1016/j.finel.2007.08.012.
  • 10. F. Bobaru, W. Hu, The meaning, selection, and use of the peridynamic horizon and its relation to crack branching in brittle materials, International Journal of Fracture, 176, 215–222, 2012, doi: 10.1007/s10704-012-9725-z.
  • 11. S.A. Silling, R.B. Lehoucq, Convergence of peridynamics to classical elasticity theory, Journal of Elasticity, 93, 13–37, 2008, doi: 10.1007/s10659-008-9163-3.
  • 12. F. Bobaru, J.T. Foster, P.H. Geubelle, S.A. Silling, Handbook of Peridynamic Modeling, CRC Press, Boca Raton, 2017.
  • 13. W. Liu, J. W. Hong, Discretized peridynamics for linear elastic solids, Computational Mechanics, 50, 579–590, 2012, doi: 10.1007/s00466-012-0690-1.
  • 14. V.V. Nishawala, M. Ostoja-Starzewski, Peristatic solutions for finite one- and twodimensional systems, Mathematics and Mechanics of Solids, 22, 1639–1653, 2017, doi: 10.1177/1081286516641180.
  • 15. M.L. Parks, R.B. Lehoucq, S.J. Plimpton, S.A. Silling, Implementing peridynamics within a molecular dynamics code, Computer Physics Communications, 179, 777–783, 2008, doi: 10.1016/j.cpc.2008.06.011.
  • 16. B. Kilic, E. Madenci, An adaptive dynamic relaxation method for quasi-static simulations using the peridynamic theory, Theoretical and Applied Fracture Mechanics, 53, 194–201, 2010, doi: 10.1016/j.tafmec.2010.08.001.
  • 17. E. Oterkus, E. Madenci, O. Weckner, S. A. Silling, P. Bogert, A. Tessler, Combined finite element and peridynamic analyses for predicting failure in a stiffened composite curved panel with a central slot, Composite Structures, 94, 839–850, 2012, doi: 10.1016/j.compstruct.2011.07.019.
  • 18. C.T. Wu, B. Ren, Localized particle boundary condition enforcements for the state based peridynamics, Coupled Systems Mechanics, 4, 1–18, 2015, doi: 10.12989/csm.2015.4.1.001.
  • 19. C.T. Wu, W. Hu, Meshfree-enriched simplex elements with strain smoothing for the finite element analysis of compressible and nearly incompressible solids, Computer Methods in Applied Mechanics & Engineering, 200, 2991–3010, 2011, doi: 10.1016/j.cma.2011.06.013.
  • 20. J.K. Chen, Y. Tian, X.Z. Cui, Free and forced vibration analysis of peridynamic finite bar, International Journal of Applied Mechanics, 2018, doi: 10.1142/S1758825118500035.
  • 21. E. Madenci, E. Oterkus, Peridynamic Theory and Its Applications, Springer, New York, 2014.
  • 22. G.A. Holzapfel, Nonlinear solid mechanics: a continuum approach for engineering science, Meccanica, 37, 489–490, 2002. doi: 10.1023/A:1020843529530.
  • 23. Y. Mikata, Analytical solutions of peristatic and peridynamic problems for a 1d Infinite rod, International Journal of Solids and Structures, 49, 2887–2897, 2012, doi: 10.1016/j.ijsolstr.2012.02.012.
  • 24. M. H. Liu, Q. Wang, W. Lu, Peridynamic simulation of brittle-ice crushed by a vertical structure, International Journal of Naval Architecture and Ocean Engineering, 9, 209–218, 2017, doi: 10.1016/j.ijnaoe.2016.10.003.
  • 25. F. Bobaru, M. Yang, L.F. Alves, S.A. Silling, E. Askari, J. Xu, Convergence, adaptive refinement, and scaling in 1D peridynamics, International Journal for Numerical Methods in Engineering, 77, 852–877, 2009, doi: 10.1002/nme.2439.
  • 26. Y.D. Ha, F. Bobaru, Studies of dynamic crack propagation and crack branching with peridynamic, International Journal of Fracture, 162, 229–244, 2010, doi: 10.1007/s10704-010-9442-4.
  • 27. X.B. Gu, X.P. Zhou, X. Xu, Numerical simulation of high-speed crack propagating and branching phenomena based on peridynamics, Applied Mathematics and Mechanics-English Edition, 37, 729–739, 2016, doi: 10.21656/1000-0887.360310.
  • 28. X.B. Gu, X.P. Zhou, The numerical simulation of tensile plate with circular hole using peridynamic theory, Chinese Journal of Solid Mechanics, 36, 376–383, 2015 [in Chinese], doi: 10.19636/j.cnki.cjsm42-1250/o3.2015.05.002.
  • 29. D.P. Rooke, D.J. Cartwright, Compendium of Stress Intensity Factors, Her Majesty’s Stationery Office, London, 1976.
Uwagi
This work has been jointly supported by the National Natural Science Foundation of China (Grant No. 12072145 and 11672129).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c38c0e0d-c4b1-4ec6-ae42-9c19d5fed127
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