Aerotecnica Missili & Spazio

, Volume 96, Issue 1, pp 44–55 | Cite as

Discontinuous mechanical problems studied with a peridynamics-based approach

  • M. Zaccariotto
  • G. Sarego
  • D. Dipasquale
  • A. Shojaei
  • S. Bazazzadeh
  • T. Mudric
  • M. Duzzi
  • U. Galvanetto


The description of crack propagation in structural materials is still a great challenge because the discontinuous nature of the phenomena conflicts with the underlying mathematical structure of classical continuum mechanics. Recently a new non-local continuum theory has been proposed, Peridynamics, with the specific goal to overcome the limitations of the classical theory. Peridynamics is based on integral equations and does not make use of spatial differentiation, for these reasons it is better suited to describe problems affected by discontinuities. The paper presents a series of applications of peridynamics-based computational methods to the solution of static and dynamic structural problems.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Y. Mi, M. A. Crisfield, G. A. O Davies and H. B. Hellweg, “Progressive delamination using interface elements”, J Compos Mater, Vol. 32, pp. 1246–1272, 1998.CrossRefGoogle Scholar
  2. 2.
    T. Belytschko, H. Chen, J. X. Xu and G. Zi, “Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment”, Int J Numer Meth Eng, Vol. 58, pp. 1873–1905, 2003.CrossRefGoogle Scholar
  3. 3.
    C. Miehe, M. Hofacker, and F. Welschinger, “A phase field model for rate-independent crack propagation:Robust algorithmic implementation based on operator splits”, Comput. Methods Appl. Mech. Eng., Vol. 119, pp. 2765–2778, 2010.MathSciNetCrossRefGoogle Scholar
  4. 4.
    M. J. Borden, C. V. Verhoosel, M. A. Scott, T. J. R. Hughes, and C. M. Landis, “A phase-field description of dynamic brittle fracture,”, Comput. Methods Appl. Mech. Eng., Vol. 217–210, pp. 77–95, 2012.MathSciNetCrossRefGoogle Scholar
  5. 5.
    L. Kosteski, B. R. D’Ambra, and I. Iturrioz, “Crack propagation in elastic solids using the truss-like discrete element method”, Int J Fract, Vol. 174, pp. 139–161, 2012.CrossRefGoogle Scholar
  6. 6.
    S. Silling, “Reformulation of elasticity theory for discontinuities and long-range forces”, J Mech Phys Solids, Vol. 48, pp. 175–209, 2000.MathSciNetCrossRefGoogle Scholar
  7. 7.
    S. Silling, M. Epton, O. Weckner, J. Xu and E. Askari, “Peridynamic states and costitutive modeling”, J Elast, Vol. 88, pp. 151–184, 2007.CrossRefGoogle Scholar
  8. 8.
    S. Oterkus, E. Madenci, A. Agwai, “Fully coupled peridynamic thermomechanics”, J Mech Phys Solids, Vol. 64, pp. 1–23, 2014.MathSciNetCrossRefGoogle Scholar
  9. 9.
    A. Katiyar, J. T. Foster, H. Ouchi and M. Sharma, “A peridynamic formulation of pressure driven convective fluid transport in porous media”, J Comput Phys, Vol. 261, pp. 209–229, 2014.MathSciNetCrossRefGoogle Scholar
  10. 10.
    M. Zaccariotto, F. Luongo, G. Sarego and U. Galvanetto, “Examples of applications of the peridynamic theory to the solution of static equilibrium problems”, The Aeronautical J., Vol. 119, pp. 1–24, 2015.CrossRefGoogle Scholar
  11. 11.
    M. Duzzi, M. Zaccariotto, U. Galvanetto, “Application of Peridynamic Theory to Nanocomposite Materials”, Adv Mat Research, Vol. 1016, pp. 44–48, 2014.Google Scholar
  12. 12.
    D. Dipasquale, M. Zaccariotto, U. Galvanetto, “Crack propagation with adaptive grid refinement in 2D peridynamics”, Int. J. of Fracture, Vol. 190, No 1–2, pp. 1–22, 2014.CrossRefGoogle Scholar
  13. 13.
    Y. D. Ha, F. Bobaru, “Characteristics of dynamic brittle fracture captured with peridynamics”, Eng. Frac. Mech, Vol. 78, No 6, pp. 1156–1168, 2011.CrossRefGoogle Scholar
  14. 14.
    W. Hu, Y. Wang, J. Yu, C. F. Yen and F. Bobaru, “Impact damage on a thin glass plate with a thin polycarbonate backing”, Int. J Imp. Eng., Vol. 62, pp. 152–165, 2013.CrossRefGoogle Scholar
  15. 15.
    E. Budyn, G. Zi, N. Moes and T. Belytschko, “A method for multiple crack growth in the brittle materials without remeshing”, Int. J. Num. Meth. Engin., Vol. 61, pp. 1741–1770, 2004.CrossRefGoogle Scholar
  16. 16.
    E. Askari, F. Bobaru, R. Lehoucq, M. Parks, S. A. Silling and O. Weckner, “Peridynamics for multiscale materials modeling”, J Phys Conf Ser, Vol. 125, pp. 1–11, 2008.CrossRefGoogle Scholar
  17. 17.
    R. Rahman, J. T. Foster, “Bridging the length scales through nonlocal hierarchical multiscale modeling scheme”, Computational Materials Science, Vol. 92, pp. 401–415, 2014.CrossRefGoogle Scholar
  18. 18.
    V. P. Nguyen, M. Stroeven and L. J. Sluys, “Multiscale continuous modeling of heterogeneous materials: a review on recent developments”, J. Multiscale Modelling, Vol. 3, No 4, pp. 1–42, 2011.MathSciNetCrossRefGoogle Scholar
  19. 19.
    D. L. Shi, X. Q. Feng, Y. Y. Huang, K. C. Hwang and H. Gao, “The effect of Nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced compositess”, J. Eng. Mater. Technol., Vol. 126, No 3, pp. 250–257, 2004.CrossRefGoogle Scholar
  20. 20.
    Y. L. Hu, E. Madenci,“Bond-based peridynamic modeling of composite laminates with arbitrary fiber orientation and stacking sequence”, Composite Struct, Vol. 153, pp. 139–175, 2016.CrossRefGoogle Scholar
  21. 21.
    Y. L. Hu, N. V. De Carvalho, E. Madenci,“Peridynamic modeling of delamination growth in composite laminates”, Composite Struct, Vol. 132, pp. 610–620, 2015.CrossRefGoogle Scholar
  22. 22.
    Y. L. Hu, Y. Yu, H. Wang,“Peridynamic analytical method for progressive damage in notched composite laminates”, Composite Struct, Vol. 108, pp. 801–810, 2014.CrossRefGoogle Scholar
  23. 23.
    S. A. Silling, E. Askari, “A meshfree method based on the peridynamic model of solid mechanics”, Comput Struct, Vol. 83, pp. 1526–1535, 2005.CrossRefGoogle Scholar
  24. 24.
    M. B. Nooru-Mohamed, E. Schlangen and J. G. M. Van Mier, “Experimental and numerical study on the behavior of concrete subjected to biaxial tension and shear”, Advanced cement based materials, Vol. 1, No 1, pp. 22–37, 1993.CrossRefGoogle Scholar
  25. 25.
    R. W. Macek, S. A. Silling, “Peridynamics via finite element analysis”, Finite Elements in Analysis and Design, Vol. 43, pp. 1169–1178, 2007.MathSciNetCrossRefGoogle Scholar
  26. 26.
    ABAQUS-Explicit Version 6. 6 User’s Manual, ABAQUS Inc., Providence, Rhode Island, 2006.Google Scholar
  27. 27.
    B. Kilic and E. Madenci, “Coupling of peridynamic theory and the finite element method”, J. of Mech. of Mat. and Struct., Vol. 5, No 5, pp. 707–733, 2010.CrossRefGoogle Scholar
  28. 28.
    W. Liu and J. W. Hong, “A coupling approach of discretized peridynamics with finite element method”, Comp. Meth. in Appl. Mech. and Eng., Vol. 245–246, pp. 163–175, 2012.MathSciNetCrossRefGoogle Scholar
  29. 29.
    G. Lubineau, Y. Azdoud, F. Han, C. Rey and A. Askari, “A morphing strategy to couple non-local to local continuum mechanics”, J. Mech. and Ph. of Solids, Vol. 60, No 6, pp. 1088–1102, 2012.MathSciNetCrossRefGoogle Scholar
  30. 30.
    A. Shojaei, B. Boroomand, and F. Mossaiby, “A simple meshless method for challenging engineering problems”, Eng. Comput., Vol. 32, No 6, pp. 1567–1600, 2015.CrossRefGoogle Scholar
  31. 31.
    W. H. Gerstle, N. Sau, and S. A. Silling, “Peridynamic modeling of plain and reinforced concrete structures”, 18th International Conference on Structural Mechanics in Reactor Technology, Beijing, China, 2005.Google Scholar
  32. 32.
    U. Galvanetto, T. Mudric, A. Shojaei, M. Zaccariotto, “An effective way to couple FEM meshes and Peridynamics grids for the solution of static equilibrium problems”, Mech Res Comm, Vol. 76, pp. 41–47, 2016.CrossRefGoogle Scholar
  33. 33.
    M. Zaccariotto, D. Tomasi, U. Galvanetto, “An enhanced coupling of PD grids to FE meshes”, Mech Res Comm, in press, 2017.Google Scholar
  34. 34.
    M. Zaccariotto, T. Mudric, D. Tomasi, A. Shojaei U. Galvanetto, “Coupling of FEM meshes with Peridynamic grids”, submitted for publication.Google Scholar
  35. 35.
    R. H. J. Peerlings, W. A. M. Brekelmans, R. de Borst and M. G. D. Geers, “Gradient-enhanced damage modelling of highcycle fatigue”, Int. J. Num. Meth. Engin., Vol. 49, No 12, pp. 1547–1569, 2000.CrossRefGoogle Scholar
  36. 36.
    U. Galvanetto, P. Robinson, A. Cerioni and C. L. Armas, “A Simple Model for the Evaluation of Constitutive Laws for the Computer Simulation of Fatigue-Driven Delamination in Composite Materials”, SDHM, Vol. 5, No 2, pp. 161–189, 2009.Google Scholar
  37. 37.
    M. Zaccariotto, F. Luongo, G. Sarego, D. Dipasquale and U. Galvanetto, “Fatigue Crack Propagation with Peridynamics: a sensitivity study of Paris law parameters”, CEAS 2013, Innov Eur Sweden, Linkoping, Sweden 2013.Google Scholar

Copyright information

© AIDAA Associazione Italiana di Aeronautica e Astronautica 2017

Authors and Affiliations

  • M. Zaccariotto
    • 1
  • G. Sarego
    • 1
  • D. Dipasquale
    • 1
  • A. Shojaei
    • 1
  • S. Bazazzadeh
    • 1
  • T. Mudric
    • 1
  • M. Duzzi
    • 1
  • U. Galvanetto
    • 1
  1. 1.Dipartimento di Ingegneria Industriale and Cisas “G. Colombo”Università di PadovaItaly

Personalised recommendations