Computational Mechanics

, Volume 57, Issue 6, pp 921–929 | Cite as

A meshfree method for bending and failure in non-ordinary peridynamic shells

Original Paper

Abstract

The peridynamic theory of solid mechanics offers an integral based alternative to traditional continuum models based on partial differential equations. This formulation is particularly advantageous when applied to material failure problems that result in discontinuous displacement fields. This paper presents a meshfree implementation of a state-based peridynamic bending model based on the idea of rotational springs between pairs of peridynamic bonds. Energy-based analysis determines the properties of these bond pairs for a brittle material, resulting in a constitutive model that naturally gives rise to localized damage and crack propagation.

Keywords

Peridynamics Brittle Beam Plate  Non-ordinary Failure Non-local  Plates Shells 

Notes

Acknowledgments

This work was funded by grant number W911NF-11-1-0208 from the United States Air Force Office of Scientific Research.

References

  1. 1.
    Bessa M, Foster J, Belytschko T, Liu WK (2014) A meshfree unification: reproducing kernel peridynamics. Comput Mech 53(6):1251–1264MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Foster J, Silling S, Chen W (2010) Viscoplasticity using peridynamics. Int J Numer Methods Eng 81(10):1242–1258. doi:10.1002/nme.2725
  3. 3.
    Foster J, Silling SA, Chen W (2011) An energy based failure criterion for use with peridynamic states. Int J Multiscale Comput Eng 9(6):675–988. doi:10.1615/IntJMultCompEng.2011002407
  4. 4.
    Fuller E Jr (1979) An evaluation of double torsion testing-analysis. Fract Mech Appl Brittle Mater ASTM STP 678:3–18CrossRefGoogle Scholar
  5. 5.
    Moyer ET, Miraglia MJ (2014) Peridynamic solutions for timoshenko beams. Engineering 6(06):304. doi:10.4236/eng.2014.66034 CrossRefGoogle Scholar
  6. 6.
    O’Grady J, Foster JT (2014) Peridynamic beams: a non-ordinary, state-based model. Int J Solids Struct 51(18):3177–3183. doi:10.1016/j.ijsolstr.2014.05.014 CrossRefGoogle Scholar
  7. 7.
    O’Grady J, Foster JT (2014) Peridynamic plates and flat shells: a non-ordinary, state-based model. Int J Solids Struct 51(25):4572–4579. doi:10.1016/j.ijsolstr.2014.09.003 CrossRefGoogle Scholar
  8. 8.
    Sala M, Spotz WF, Heroux MA (2008) PyTrilinos: high-perfor-mance distributed-memory solvers for Python. ACM Trans Math Softw (TOMS) 34(2):1–33Google Scholar
  9. 9.
    Silling S (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48(1):175–209. doi:10.1016/S0022-5096(99)00029-0 MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Silling S, Epton M, Weckner O, Xu J, Askari E (2007) Peridynamic states and constitutive modeling. J Elast 88(2):151–184. doi:10.1007/s10659-007-9125-1 MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Silling SA, Askari E (2005) A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83(17):1526–1535. doi:10.1016/j.compstruc.2004.11.026 CrossRefGoogle Scholar
  12. 12.
    Taylor M, Steigmann DJ (2013) A two-dimensional peridynamic model for thin plates. Math Mech Solids. doi:10.1177/1081286513512925

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.The University of Texas at Austin, Petroleum & Geosystems EngineeringAustinUSA

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