Skip to main content
SpringerLink
Log in

A peridynamic failure analysis of fiber-reinforced composite laminates using finite element discontinuous Galerkin approximations

  • Original Paper
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

This paper presents a discontinuous Galerkin weak form for bond-based peridynamic models to predict the damage of fiber-reinforced composite laminates. To represent the anisotropy of a laminate in a peridynamic model, a lamina is simplified as a transversely isotropic medium under a plane stress condition. The laminated structure is modeled by stacking the surface mesh layers along the thickness direction according to the laminate sequence. To avoid a mesh dependence on either the fiber orientation or the discretization, the spherical harmonic expansion theory is employed to construct a function for the micro-elastic modulus in terms of the bond-fiber angle. The laminate material is decomposed into an isotropic matrix material part and a transversely isotropic material part. The bond stiffness can be evaluated using the engineering material constants, based on the equivalence between the elastic energy density in the peridynamic theory and the elastic energy density in the classic continuum mechanics theory. Benchmark tests are conducted to verify the proposed model. Numerical results illustrate that the convergence of simulations with different horizon sizes and meshes can be achieved. In terms of damage analysis, the proposed model can capture the dynamic process of the complex coupling of the inner-layer and delamination damage modes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

References

  • Azdoud Y, Han F, Lubineau G (2014) The morphing method as a flexible tool for adaptive local/non-local simulation of static fracture. Comput Mech 54:711–722

    Article  Google Scholar 

  • Belytschko T, Lin JI (1987) A three-dimensional impact-penetration algorithm with erosion. Int J Impact Eng 5:111–127

    Article  Google Scholar 

  • Bobaru F, Hu W (2012) The meaning, selection, and use of the peridynamic horizon and its relation to crack branching in brittle materials. Int J Fract 176:215–222

    Article  Google Scholar 

  • Chen X, Gunzburger M (2011) Continuous and discontinuous finite element methods for a peridynamics model of mechanics. Comput Methods Appl Mech Eng 200:1237–1250

    Article  Google Scholar 

  • Chen JS, Wu CT, Belytschko T (2000) Regularization of material instabilities by meshfree approximations with intrinsic length scales. Int J Numer Methods Eng 47:1303–1322

    Article  Google Scholar 

  • Foster JT, Silling SA, Chen WW (2010) Viscoplasticity using peridynamics. Int J Numer Methods Eng 81:1242–1258

    Google Scholar 

  • Gerstle W, Sau N, Silling SA (2007) Peridynamic modeling of concrete structures. Nucl Eng Des 237:1250–1258

    Article  CAS  Google Scholar 

  • Ghajari M, Iannucci L, Curtis P (2014) A peridynamic material model for the analysis of dynamic crack propagation in orthotropic media. Comput Methods Appl Mech Eng 276:431–452

    Article  Google Scholar 

  • Han F, Lubineau G, Azdoud Y, Askari A (2016) A morphing approach to couple state-based peridynamics with classical continuum mechanics. Comput Methods Appl Mech Eng 301:336–358

    Article  Google Scholar 

  • Hu YL, Madenci E (2016) Bond-based peridynamic modeling of composite laminates with arbitrary fiber orientation and stacking sequence. Compos Struct 153:139–175

    Article  Google Scholar 

  • Hu W, Ha YD, Bobaru F (2011) Modeling dynamic fracture and damage in a fiber-reinforced composite lamina with peridynamics. Int J Multiscale Comput Eng 9(6):707–726

    Article  Google Scholar 

  • Hu W, Ha YD, Bobaru F (2012) Peridynamic model for dynamic fracture in unidirectional fiber-reinforced composites. Comput Methods Appl Mech Eng 217–220:247–261

    Article  Google Scholar 

  • Hu YL, Yu Y, Wang H (2014) Peridynamic analytical method for progressive damage in notched composite laminates. Compos Struct 108:801–810

    Article  Google Scholar 

  • Hu YL, Carvalho NV, Madenci E (2015) Peridynamic modeling of delamination growth in composite laminates. Compos Struct 132:610–620

    Article  Google Scholar 

  • Johnson GR, Stryk RA (1987) Eroding interface and improved tetrahedral element algorithms for high-velocity impact computations in three dimensions. Int J Impact Eng 5:411–421

    Article  Google Scholar 

  • Kaminski MM (2005) Computational mechanics of composite materials. Springer-Verlag, London

    Google Scholar 

  • Kilic B, Madenci E, Ambur DR (2006) Analysis of brazed single-lap joints using the peridynamics theory. In: 47th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference. Newport, Rhode Island

  • Kröner E (1967) Elasticity theory of materials with long range cohesive forces. Int J Solids Struct 3:731–742

    Article  Google Scholar 

  • Lai X, Ren B, Fan H, Li S, Wu CT, Regueiro RA, Liu L (2015) Peridynamics simulations of geomaterial fragmentation by impulse loads. Int J Numer Anal Methods Geomech 39:1304–1330

    Article  Google Scholar 

  • Lehoucq RB, Silling SA (2008) Force flux and the peridynamic stress tensor. J Mech Phys Solids 56:1566–1577

    Article  Google Scholar 

  • Liu Z, Bessa MA, Liu WK (2016) Self-consistent clustering analysis: an efficient multi-scale scheme for inelastic heterogeneous materials. Comput Methods Appl Mech Eng 306:319–341

    Article  Google Scholar 

  • Madenci E, Oterkus E (2014) Peridynamic theory and its applications. Springer, New York

    Book  Google Scholar 

  • Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–150

    Article  Google Scholar 

  • Oterkus E (2010) Peridynamic theory for modeling three-dimensional damage growth in metallic and composite structures. Ph.D. Dissertation, Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, AZ

  • Ren B, Li S (2012) Modeling and simulation of large-scale ductile fracture in plates and shells. Int J Solids Struct 49:2373–2393

    Article  Google Scholar 

  • Ren B, Wu CT, Askari E (2017) A 3D discontinuous Galerkin finite element method with the bond-based peridynamics model for dynamic brittle failure analysis. Int J Impact Eng 99:14–25

    Article  Google Scholar 

  • Seleson P, Littlewood DJ (2016) Convergence studies in meshfree peridynamic simulations. Comput Math Appl 71:2432–2448

    Article  Google Scholar 

  • Seleson P, Parks ML (2011) On the role of the influence function in the peridynamic theory. Int J Multiscale Comput Eng 9(6):689–706

    Article  Google Scholar 

  • Seleson P, Gunzburger M, Parks ML (2013) Interface problems in nonlocal diffusion and sharp transitions between local and nonlocal domains. Comput Methods Appl Mech Eng 266:185–204

    Article  Google Scholar 

  • Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48:175–209

    Article  Google Scholar 

  • Silling SA, Askari E (2005) A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83:1526–1535

    Article  Google Scholar 

  • Silling SA, Epton M, Weckner O, Xu J, Askari E (2007) Peridynamic states and constitutive modeling. J Elast 88:151–184

    Article  Google Scholar 

  • Wu CT, Ren B (2015) A stabilized non-ordinary state-based peridynamics for the nonlocal ductile material failure analysis in metal machining process. Comput Methods Appl Mech Eng 291:197–215

    Article  Google Scholar 

  • Wu CT, Ma N, Takada K, Okada H (2016) A meshfree continuous-discontinuous approach for the ductile fracture modeling in explicit dynamics analysis. Comput Mech 58:391–409

    Article  Google Scholar 

  • Xu XP, Needleman A (1994) Numerical simulations of fast crack growth in brittle solids. J Mech Phys Solid 42:1397–1434

    Article  Google Scholar 

  • Xu J, Askari A, Weckner O, Silling SA (2008) Peridynamic analysis of impact damage in composite laminates. J Aerosp Eng 21:187–194

    Article  Google Scholar 

  • Zhang B (2016) Grain-scale computational modeling of quasi-static and dynamic loading on natural soils. Ph.D. Thesis, Department of Civil, Environmental, and Architectural Engineering, University of Colorado at Boulder

Download references

Acknowledgements

This work was sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory (ORNL), managed by UT-Battelle, LLC, for the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. The authors would also like to thank Dr. John O. Hallquist from Livermore Software Technology Corporation for his support to this research. Helpful discussions with Dr. Stewart Silling from Sandia National Laboratories, New Mexico, as well as with Dr. Mazdak Ghajari from Imperial College are gratefully acknowledged.

Author information

Authors and Affiliations

  1. Livermore Software Technology Corporation, 7374 Las Positas Road, Livermore, CA, 94551-5110, USA

    Bo Ren & C. T. Wu

  2. Computer Science and Mathematics Division, Oak Ridge National Laboratory, One Bethel Valley Road, P.O. Box 2008, MS-6211, Oak Ridge, TN, 37831-6211, USA

    Pablo Seleson

  3. Ford Motor Company, Ford Research and Innovation Center, 2101 Village Road, Dearborn, MI, 48124-3993, USA

    Danielle Zeng

  4. Department of Civil and Environmental Engineering, The University of California, Berkeley, CA, 94720-1710, USA

    Dandan Lyu

Authors
  1. Bo Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. T. Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pablo Seleson
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Danielle Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Dandan Lyu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. T. Wu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ren, B., Wu, C.T., Seleson, P. et al. A peridynamic failure analysis of fiber-reinforced composite laminates using finite element discontinuous Galerkin approximations. Int J Fract 214, 49–68 (2018). https://doi.org/10.1007/s10704-018-0317-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-018-0317-4

Keywords

Search

Navigation