Predicting single-lap joint strength using the natural neighbour radial point interpolation method

  • L. D. C. Ramalho
  • R. D. S. G. CampilhoEmail author
  • J. BelinhaEmail author
Technical Paper


The increased usage of adhesive joints over traditional joining techniques results in a need to develop good designing tools for this type of joint. The most common method to predict adhesive joint strength is cohesive zone models (CZMs). CZMs use traction–separation laws that define the adhesive behaviour, which needs to be determined experimentally. However, these laws are dependent on the adhesive thickness (tA), so they have to be measured several times when predicting the strength of joints with different tA values. Recently, the critical longitudinal strain (CLS) criterion, based on continuum mechanics, was proposed and used with the finite element method to predict the strength of single-lap joints (SLJs) with good accuracy. The use of meshless methods to predict the strength of adhesive joints is currently very limited. To address this, in the present work the strength of SLJ was predicted using the CLS criterion combined with the natural neighbour radial point interpolation method. The strength predictions resulting from this approach were accurate for three different adhesives, ranging from brittle to very ductile.


Finite element method Meshless methods Adhesive joints Structural adhesive 



The authors truly acknowledge the funding provided by Ministério da Ciência, Tecnologia e Ensino Superior—Fundação para a Ciência e a Tecnologia (Portugal), under project funding MIT-EXPL/ISF/0084/2017 and POCI-01-0145-FEDER-028351. Additionally, the authors gratefully acknowledge the funding of Project NORTE-01-0145-FEDER-000022-SciTech-Science and Technology for Competitive and Sustainable Industries, co-financed by Programa Operacional Regional do Norte (NORTE2020), through Fundo Europeu de Desenvolvimento Regional (FEDER).


  1. 1.
    Marques GP, Campilho RDSG, Da Silva FJG, Moreira RDF (2016) Adhesive selection for hybrid spot-welded/bonded single-lap joints: experimentation and numerical analysis. Compos Part B Eng 84:248–257CrossRefGoogle Scholar
  2. 2.
    Arouche MM, Budhe S, Alves LA, Teixeira de Freitas S, Banea MD, de Barros S (2018) Effect of moisture on the adhesion of CFRP-to-steel bonded joints using peel tests. J Braz Soc Mech Sci Eng 40:1CrossRefGoogle Scholar
  3. 3.
    Teixeira JMD, Campilho RDSG, da Silva FJG (2018) Numerical assessment of the double-cantilever beam and tapered double-cantilever beam tests for the GIC determination of adhesive layers. J Adhes 94(11):951–973CrossRefGoogle Scholar
  4. 4.
    Volkersen O (1938) Die Nietkraftverteilung in zugbeanspruchten Nietverbindungen mit konstanten Laschenquerschnitten. Luftfahrtfor schung 15:41–47Google Scholar
  5. 5.
    Goland M, Reissner E (1944) The stresses in cemented joints. J Appl Mech 17:66Google Scholar
  6. 6.
    da Silva LFM, das Neves PJC, Adams RD, Spelt JK (2009) Analytical models of adhesively bonded joints-part I: literature survey. Int J Adhes Adhes 29(3):319–330CrossRefGoogle Scholar
  7. 7.
    da Silva LFM, das Neves PJC, Adams RD, Wang A, Spelt JK (2009) Analytical models of adhesively bonded joints-part II: comparative study. Int J Adhes Adhes 29(3):331–341CrossRefGoogle Scholar
  8. 8.
    Le Pavic J, Stamoulis G, Bonnemains T, Da Silva D, Thévenet D (2019) Fast failure prediction of adhesively bonded structures using a coupled stress-energetic failure criterion. Fatigue Fract Eng Mater Struct 42(42):627–639CrossRefGoogle Scholar
  9. 9.
    Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1):131–150MathSciNetCrossRefGoogle Scholar
  10. 10.
    Alves DL, Campilho RDSGSG, Moreira RDFF, Silva FJGG, Silva LFM, da Silva LFM (2018) Experimental and numerical analysis of hybrid adhesively-bonded scarf joints. Int J Adhes Adhes 83(May):87–95CrossRefGoogle Scholar
  11. 11.
    Sane AU, Padole PM, Manjunatha CM, Uddanwadiker RV, Jhunjhunwala P (2018) Mixed mode cohesive zone modelling and analysis of adhesively bonded composite T-joint under pull-out load. J Braz Soc Mech Sci Eng 40:3CrossRefGoogle Scholar
  12. 12.
    Silva JOS, Campilho RDSG, Rocha RJB (2018) Crack growth analysis of adhesively-bonded stepped joints in aluminium structures. J Braz Soc Mech Sci Eng 40(11):540CrossRefGoogle Scholar
  13. 13.
    Ji G, Ouyang Z, Li G, Ibekwe S, Pang SS (2010) Effects of adhesive thickness on global and local mode-I interfacial fracture of bonded joints. Int J Solids Struct 47(18–19):2445–2458CrossRefGoogle Scholar
  14. 14.
    da Silva LFM, de Magalhães FACRG, Chaves FJP, De Moura MFSF (2010) Mode II fracture toughness of a brittle and a ductile adhesive as a function of the adhesive thickness. J Adhes 86(9):889–903CrossRefGoogle Scholar
  15. 15.
    Ji G, Ouyang Z, Li G (2012) Local interface shear fracture of bonded steel joints with various bondline thicknesses. Exp Mech 52(5):481–491CrossRefGoogle Scholar
  16. 16.
    Ji G, Ouyang Z, Li G (2012) On the interfacial constitutive laws of mixed mode fracture with various adhesive thicknesses. Mech Mater 47:24–32CrossRefGoogle Scholar
  17. 17.
    da Silva LFM, Campilho RDSG (2012) Advances in numerical modeling of adhesive joints. Springer, New YorkCrossRefGoogle Scholar
  18. 18.
    Harris JA, Adams RA (1984) Strength prediction of bonded single lap joints by non-linear finite element methods. Int J Adhes Adhes 4(2):65–78CrossRefGoogle Scholar
  19. 19.
    Ayatollahi MR, Akhavan-Safar A (2015) Failure load prediction of single lap adhesive joints based on a new linear elastic criterion. Theor Appl Fract Mech 80:210–217CrossRefGoogle Scholar
  20. 20.
    Kim MH, Hong HS (2016) An adaptation of mixed-mode I + II continuum damage model for prediction of fracture characteristics in adhesively bonded joint. Int J Adhes Adhes 80:87–103CrossRefGoogle Scholar
  21. 21.
    Zhang Q, Cheng X, Cheng Y, Li W, Hu R (2019) Investigation of tensile behavior and influence factors of composite-to-metal 2D-scarf bonded joint. Eng Struct 180:284–294CrossRefGoogle Scholar
  22. 22.
    Stein N, Dölling S, Chalkiadaki K, Becker W, Weißgraeber P (2017) Enhanced XFEM for crack deflection in multi-material joints. Int J Fract 207(2):193–210CrossRefGoogle Scholar
  23. 23.
    Belinha J (2014) Meshless methods in biomechanics. Springer, New YorkCrossRefGoogle Scholar
  24. 24.
    Dinis LMJS, Natal Jorge RM, Belinha J (2007) Analysis of 3D solids using the natural neighbour radial point interpolation method. Comput Methods Appl Mech Eng 196(13–16):2009–2028CrossRefGoogle Scholar
  25. 25.
    Braun J, Sambridge M (1995) A numerical method for solving partial differential equations on highly irregular evolving grids. Nature 376(6542):655–660CrossRefGoogle Scholar
  26. 26.
    Wang JG, Liu GR (2002) A point interpolation meshless method based on radial basis functions. Int J Numer Methods Eng 54(11):1623–1648CrossRefGoogle Scholar
  27. 27.
    Lucy LB (1977) A numerical approach to the testing of the fission hypothesis. Astron J 82(December):1013–1024CrossRefGoogle Scholar
  28. 28.
    Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc 181(3):375–389CrossRefGoogle Scholar
  29. 29.
    Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin methods. Int J Numer Methods Eng 37(2):229–256MathSciNetCrossRefGoogle Scholar
  30. 30.
    Liu WK, Jun S, Zhang YF (1995) Reproducing kernel particle methods. Int J Numer Methods Fluids 20(8–9):1081–1106MathSciNetCrossRefGoogle Scholar
  31. 31.
    Tsai CL, Guan YL, Ohanehi DC, Dillard JG, Dillard DA, Batra RC (2014) Analysis of cohesive failure in adhesively bonded joints with the SSPH meshless method. Int J Adhes Adhes 51:67–80CrossRefGoogle Scholar
  32. 32.
    Bodjona K, Lessard L (2015) Nonlinear static analysis of a composite bonded/bolted single-lap joint using the meshfree radial point interpolation method. Compos Struct 134:1024–1035CrossRefGoogle Scholar
  33. 33.
    Mubashar A, Ashcroft IA (2017) Comparison of cohesive zone elements and smoothed particle hydrodynamics for failure prediction of single lap adhesive joints. J Adhes 93(6):444–460CrossRefGoogle Scholar
  34. 34.
    Akhavan-Safar A, da Silva LFM, Ayatollahi MR (2017) An investigation on the strength of single lap adhesive joints with a wide range of materials and dimensions using a critical distance approach. Int J Adhes Adhes 78:248–255CrossRefGoogle Scholar
  35. 35.
    Akhavan-Safar A, Ayatollahi MR, da Silva LFM (2017) Strength prediction of adhesively bonded single lap joints with different bondline thicknesses: a critical longitudinal strain approach. Int J Solids Struct 109:189–198CrossRefGoogle Scholar
  36. 36.
    Khoramishad H, Akhavan-Safar A, Ayatollahi MR, Da Silva LFM (2017) Predicting static strength in adhesively bonded single lap joints using a critical distance based method: Substrate thickness and overlap length effects. Proc Inst Mech Eng Part L J Mater Des Appl 231(1–2):237–246Google Scholar
  37. 37.
    Campilho RDSG, Pinto AMG, Banea MD, Silva RF, Da Silva LFM (2011) Strength improvement of adhesively-bonded joints using a reverse-bent geometry. J Adhes Sci Technol 25(18):2351–2368CrossRefGoogle Scholar
  38. 38.
    ASTM International (2008)ASTM E8M-04, Standard test methods for tension testing of metallic materials [metric] (Withdrawn 2008), West Conshohocken.
  39. 39.
    Neto JABP, Campilho RDSG, Da Silva LFM (2012) Parametric study of adhesive joints with composites. Int J Adhes Adhes 37:96–101CrossRefGoogle Scholar
  40. 40.
    Campilho RDSG, Banea MD, Neto JABP, Da Silva LFM (2013) Modelling adhesive joints with cohesive zone models: effect of the cohesive law shape of the adhesive layer. Int J Adhes Adhes 44(4–6):48–56CrossRefGoogle Scholar
  41. 41.
    Campilho RDSG, Moura DC, Gonçalves DJS, Da Silva JFMG, Banea MD, Da Silva LFM (2013) Fracture toughness determination of adhesive and co-cured joints in natural fibre composites. Compos Part B Eng 50:120–126CrossRefGoogle Scholar
  42. 42.
    Campilho RDSG, Moura DC, Gonçalves DJS, Da Silva JFMG, Banea MD, Da Silva LFM (2013) Fracture toughness determination of adhesive and co-cured joints in natural fibre composites. Compos Part B Eng 50:120–126CrossRefGoogle Scholar
  43. 43.
    Campilho RDSG, Banea MD, Pinto AMG, Da Silva LFM, De Jesus AMP (2011) Strength prediction of single- and double-lap joints by standard and extended finite element modelling. Int J Adhes Adhes 31(5):363–372CrossRefGoogle Scholar
  44. 44.
    Nunes SLS et al (2016) Comparative failure assessment of single and double lap joints with varying adhesive systems. J Adhes 92(7–9):610–634CrossRefGoogle Scholar
  45. 45.
    Adams RD (2005) Adhesive bonding: science, technology and applications. Woodhead Publishing Limited, CambridgeCrossRefGoogle Scholar
  46. 46.
    Adams RD, Peppiatt NA (1974) Stress analysis of adhesive-bonded lap joints. J Strain Anal 9(3):185–196CrossRefGoogle Scholar
  47. 47.
    Davis M, Bond D (1999) Principles and practices of adhesive bonded structural joints and repairs. Int J Adhes Adhes 19(2):91–105CrossRefGoogle Scholar
  48. 48.
    Liu Z, Huang Y, Yin Z, Bennati S, Valvo PS (2014) A general solution for the two-dimensional stress analysis of balanced and unbalanced adhesively bonded joints. Int J Adhes Adhes 54:112–123CrossRefGoogle Scholar
  49. 49.
    Voronoi G (1908) Nouvelles applications des paramètres continus à la théorie des formes quadratiques Deuxième mémoire. Recherches sur les parallélloèdres primitifs. J für die reine und Angew Math 134:198–287MathSciNetzbMATHGoogle Scholar
  50. 50.
    Delaunay B (1934) Sur la sphère vide. A la mémoire de Georges Voronoï. Bull. l’Académie des Sci. l’URSS 6:793–800zbMATHGoogle Scholar
  51. 51.
    Wang JG, Liu GR (2002) On the optimal shape parameters of radial basis functions used for 2-D meshless methods. Comput Methods Appl Mech Eng 191(23–24):2611–2630MathSciNetCrossRefGoogle Scholar
  52. 52.
    Taylor D (2008) The theory of critical distances. Eng Fract Mech 75(7):1696–1705CrossRefGoogle Scholar
  53. 53.
    Liu GR (2010) Meshfree methods. CRC Press, Boca RatonGoogle Scholar
  54. 54.
    Cordes LW, Moran B (1996) Treatment of material discontinuity in the element-free Galerkin method. Comput Methods Appl Mech Eng 139(1–4):75–89CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.INEGI, Institute of Mechanical EngineeringPortoPortugal
  2. 2.School of Engineering, Polytechnic of PortoISEP-IPPPortoPortugal

Personalised recommendations