Skip to main content
SpringerLink
Log in

Peridynamic Modeling of Laminated Composites

  • Chapter
  • First Online:
Size-Dependent Continuum Mechanics Approaches

Part of the book series: Springer Tracts in Mechanical Engineering ((STME))

  • 559 Accesses

Abstract

Damage growth in composites involves complex and progressive failure modes. Current computational tools are incapable of predicting failure in composite materials in a unified manner mainly due to their mathematical structure. However, the peridynamic (PD) theory removes these obstacles by taking into account nonlocal interactions between material points. The PD theory simply replaces the displacement derivatives in the equilibrium equations. The PD enables the modeling of progressive failure during deformation through the removal of nonlocal PD interactions (bonds). These bonds enable the interaction of material points within each ply as well as their interaction with other material points in the adjacent plies. The solution continues by using standard explicit time integration techniques until final failure. This chapter presents PD modeling approaches namely bond-based, ordinary state-based, and PD differential operator for predicting progressive damage in fiber-reinforced composite materials under general loading conditions. The predictions from the PD models agree with the experimental observations published in the literature.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Krueger R (2004) Virtual crack closure technique: history, approach, and applications. Appl Mech Rev 57:109–143

    Article  Google Scholar 

  2. Liu PF, Hou SJ, Chu JK, Hu XY, Zhou CL, Liu YL, Zheng JY, Zhao A, Yan L (2011) Finite element analysis of postbuckling and delamination of composite laminates using virtual crack closure technique. Compos Struct 93:1549–1560

    Article  Google Scholar 

  3. Shokrieh MM, Rajabpour-Shirazi H, Heidari-Rarani M, Haghpanahi M (2012) Simulation of mode I delamination propagation in multidirectional composites with R-curve effects using VCCT method. Comput Mater Sci 65:66–73

    Article  Google Scholar 

  4. Borg R, Nilsson L, Simonsson K (2001) Simulation of delamination in fiber composites with a discrete cohesive failure model. Compos Sci Tech 61:667–677

    Article  Google Scholar 

  5. Yang Q, Cox B (2005) Cohesive models for damage evolution in laminated composites. Int J Fract 133:107–137

    Article  Google Scholar 

  6. Zhao L, Gong Y, Zhang J, Chen Y, Fei B (2014) Simulation of delamination growth in multidirectional laminates under mode I and mixed mode I/II loadings using cohesive elements. Compos Struct 116:509–522

    Article  Google Scholar 

  7. Rybicki EF, Kanninen MF (1977) A finite element calculation of stress intensity factors by a modified crack closure integral. Eng Fract Mech 9:931–938

    Article  Google Scholar 

  8. Dugdale DS (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8:100–104

    Article  Google Scholar 

  9. Barenblatt GI (1962) The mathematical theory of equilibrium cracks in brittle fracture. Adv Appl Mech 7:55–129

    Article  MathSciNet  Google Scholar 

  10. Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Method Eng 45:601–620

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  14. Madenci E, Oterkus E (2014) Peridynamic theory and its applications. Springer

    Google Scholar 

  15. Madenci E, Dorduncu M, Phan N, Gu X (2019) Weak form of bond-associated non-ordinary state-based peridynamics free of zero energy modes with uniform or non-uniform discretization. Eng Fract Mech 218:106613

    Article  Google Scholar 

  16. Madenci E, Dorduncu M, Barut A, Phan N (2018) A state-based peridynamic analysis in a finite element framework. Eng Fract Mech 195:104–128

    Article  Google Scholar 

  17. Askari E, Xu J, Silling S (2006) Peridynamic analysis of damage and failure in composites. In: 44th AIAA/ASME/ASCE/AHS/ASC aerospace sciences meeting and exhibit, Reno, NV. AIAA 2006-88

    Google Scholar 

  18. Xu J, Askari A, Weckner O, Razi H, Silling S (2007) Damage and failure analysis of composite laminates under biaxial loads. 48th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Honolulu, HI. AIAA 2007–2315

    Google Scholar 

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

    Article  Google Scholar 

  20. Kilic B, Agwai A, Madenci E (2009) Peridynamic theory for progressive damage prediction in center-cracked composite laminates. Compos Struct 90:141–151

    Article  Google Scholar 

  21. Oterkus E, Madenci E (2012) Peridynamic analysis of fiber-reinforced composite materials. J Mech Mater Struct 7:45–84

    Article  Google Scholar 

  22. 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 9:707–726

    Article  Google Scholar 

  23. Oterkus E, Madenci E, Weckner O, Silling S, Bogert P, Tessler A (2012) Combined finite element and peridynamic analyses for predicting failure in a stiffened composite curved panel with a central slot. Compos Struct 94:839–850

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  25. 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 

  26. 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 

  27. Diyaroglu C, Oterkus E, Madenci E, Rabczuk T, Siddiq A (2016) Peridynamic modeling of composite laminates under explosive loading. Compos Struct 144:14–23

    Article  Google Scholar 

  28. Sadowski T, Pankowski B (2016) Peridynamical modelling of nanoindentation in ceramic composites. Solid State Phenom 254:55–59

    Article  Google Scholar 

  29. Ren B, Wu CT, Seleson P, Zeng D, Lyu D (2018) A peridynamic failure analysis of fiber-reinforced composite laminates using finite element discontinuous Galerkin approximations. Int J Fract 214:49–68

    Article  Google Scholar 

  30. Diana V, Casolo S (2019) A full orthotropic micropolar peridynamic formulation for linearly elastic solids. Int J Mech Sci 160:140–155

    Article  Google Scholar 

  31. Colavito KW, Barut A, Madenci E, Phan N (2013) Residual strength of composite laminates with a hole by using peridynamic theory. 54th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, Boston, MA, AIAA-2013-1761

    Google Scholar 

  32. Jiang XW, Wang H (2018) Ordinary state-based peridynamics for open-hole tensile Strength prediction of fiber-reinforced composite laminates. J Mech Mater Struct 13:53–82

    Article  MathSciNet  Google Scholar 

  33. Jiang XW, Wang H, Shijun G (2019) Peridynamic open-hole tensile strength prediction of fiber-reinforced composite laminate using energy-based failure criteria. Adv Mater Sci Eng 2019:7694081

    Google Scholar 

  34. Zhang H, Qiao P (2019) A state-based peridynamic model for quantitative elastic and fracture analysis of orthotropic materials. Eng Fract Mech 206:147–171

    Article  Google Scholar 

  35. Gao Y, Oterkus S (2019) Fully coupled thermomechanical analysis of laminated composites by using ordinary state based peridynamic theory. Compos Struct 207:397–424

    Article  Google Scholar 

  36. Rädel M, Willberg C, Krause D (2019) Peridynamic analysis of fibre-matrix debond and matrix failure mechanisms in composites under transverse tensile load by an energy-based damage criterion. Compos. Part B 158:18–27

    Article  Google Scholar 

  37. Hattori G, Trevelyan J, Coombs WM (2018) A non-ordinary state-based peridynamics framework for anisotropic materials. Comput Method Appl Mech Eng 339:416–442

    Article  MathSciNet  Google Scholar 

  38. Yaghoobi A, Chorzepa MG (2015) Meshless modeling framework for fiber reinforced concrete structures. Comput Struct 161:43–54

    Article  Google Scholar 

  39. Shang S, Qin X, Li H, Cao X (2019) An application of non-ordinary state-based peridynamics theory in cutting process modelling of unidirectional carbon fiber reinforced polymer material. Compos Struct 226:111194

    Article  Google Scholar 

  40. Madenci E, Dorduncu M, Phan N (2018) Peridynamics for progressive failure analysis of composites. 33rd technical conference of the American society for composites, 599–613

    Google Scholar 

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

    Article  Google Scholar 

  42. Colavito KW (2013) Peridynamics for failure and residual strength prediction of fiber-reinforced composites. PhD Thesis, University of Arizona

    Google Scholar 

  43. Satyanarayana A, Bogert PA, Chunchu PB (2007) The effect of delamination on damage path and failure load prediction for notched composite laminates. 48th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Honolulu, HI. AIAA 2007-1993

    Google Scholar 

  44. Colavito KW, Kilic B, Celik E, Madenci E, Askari E, Silling S (2007) Effects of nanoparticles on stiffness and impact strength of composites. 48th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Honolulu, HI. AIAA 2007-2021

    Google Scholar 

  45. Colavito KW, Kilic B, Celik E, Madenci E, Askari E, Silling S (2007) Effect of void content on stiffness and strength of composites by a peridynamic analysis and static indentation test. 48th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Honolulu, HI. AIAA 2007-2257

    Google Scholar 

  46. Madenci E, Barut A, Futch M (2016) Peridynamic differential operator and its applications. Comput Method Appl Mech Eng 304:408–451

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ, 85715, USA

    Erdogan Madenci

  2. Department of Mechanical Engineering, Erciyes University, 38039, Kayseri, Turkey

    Mehmet Dorduncu

Authors
  1. Erdogan Madenci
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mehmet Dorduncu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Erdogan Madenci .

Editor information

Editors and Affiliations

  1. School of Mechanical Engineering, Shiraz University, Shiraz, Iran

    Esmaeal Ghavanloo

  2. School of Mechanical Engineering, Shiraz University, Shiraz, Iran

    S. Ahmad Fazelzadeh

  3. Department of Structures for Engineering and Architecture, University of Naples Federico II, Naples, Italy

    Francesco Marotti de Sciarra

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Madenci, E., Dorduncu, M. (2021). Peridynamic Modeling of Laminated Composites. In: Ghavanloo, E., Fazelzadeh, S.A., Marotti de Sciarra, F. (eds) Size-Dependent Continuum Mechanics Approaches. Springer Tracts in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-63050-8_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-63050-8_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-63049-2

  • Online ISBN: 978-3-030-63050-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation