Skip to main content

A Comparison of Delamination Models: Modeling, Properties, and Applications

  • Conference paper
  • First Online:
Book cover Mathematical Analysis of Continuum Mechanics and Industrial Applications II (CoMFoS 2016)

Part of the book series: Mathematics for Industry ((MFI,volume 30))

Included in the following conference series:

  • 532 Accesses

Abstract

This contribution presents recent results in the modeling and the analysis of delamination problems. It addresses adhesive contact, brittle, and cohesive zone models both in a quasistatic and a viscous, dynamic setting for the bulk part. Also different evolution laws for the delaminating surface are discussed.

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

Access this chapter

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

References

  1. Akagi, G., Kimura, M.: Unidirectional evolution equations of diffusion type. arXiv:1501.01072 (2015)

  2. Almi, S.: Energy release rate and quasistatic evolution via vanishing viscosity in a cohesive fracture model with an activation threshold. ESAIM Control Optim. Calc. Var. (2016). Published online

    Google Scholar 

  3. Ambati, M., Kruse, R., De Lorenzis, L.: A phase-field model for ductile fracture at finite strains and its experimental verification. Comput. Mech. 57 (2016)

    Google Scholar 

  4. Ambrosio, L., Fusco, N., Pallara, D.: Functions of Bounded Variation and Free Discontinuity Problems. Oxford University Press, New York (2005)

    Google Scholar 

  5. Artina, M., Cagnetti, F., Fornasier, M., Solombrino, F.: Linearly constrained evolutions of critical points and an application to cohesive fractures. arXiv-Preprint no. 1508.02965 (2016)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Bonetti, E., Bonfanti, G., Rossi, R.: Well-posedness and long-time behaviour for a model of contact with adhesion. Indiana Univ. Math. J. 56, 2787–2820 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bonetti, E., Bonfanti, G., Rossi, R.: Global existence for a contact problem with adhesion. Math. Meth. Appl. Sci. 31, 1029–1064 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bonetti, E., Bonfanti, G., Rossi, R.: Analysis of a temperature-dependent model for adhesive contact with friction. Phys. D 285, 42–62 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  10. Bonetti, E., Bonfanti, G., Rossi, R.: Modeling via the internal energy balance and analysis of adhesive contact with friction in thermoviscoeleasticity. Nonlinear Analysis Real World Appl. 22, 473–507 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  11. Bonetti, E., Rocca, E., Scala, R., Schimperna, G.: On the strongly damped wave equation with constraint. WIAS-Preprint 2094 (2015)

    Google Scholar 

  12. Burke, S., Ortner, C., Süli, E.: An adaptive finite element approximation of a variational model of brittle fracture. SIAM J. Numerical Analysis 48(3), 980–1012 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Cagnetti, F.: A vanishing viscosity approach to fracture growth in a cohesive zone model with prescribed crack path. Math. Models Methods Appl. Sci. 18(7), 1027–1071 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Cagnetti, F., Toader, R.: Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a young measures approach. ESAIM Control Optim. Calc. Var. 17(1), 1–27 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  15. Conti, S., Focardi, M., Iurlano, F.: Phase field approximation of cohesive fracture models. Ann. Inst. H. Poincaré Anal. Non Linéaire 33(4), 1033–1067 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  16. Conti, S., Focardi, M., Iurlano, F.: Some recent results on the convergence of damage to fracture. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 27(1), 51–60 (2016)

    Google Scholar 

  17. Dal Maso, G.: Generalised functions of bounded deformation. J. Eur. Math. Soc. 15, 1943–1997 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  18. Dal Maso, G., Larsen, C.: Existence for wave equations on domains with arbitrary growing cracks. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 22, 387–408 (2011)

    Google Scholar 

  19. Dal Maso, G., Larsen, C., Toader, R.: Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition (2015). SISSA Preprint, Trieste

    Google Scholar 

  20. Dal Maso, G., Lazzaroni, G., Nardini, L.: Existence and uniqueness of dynamic evolutions for a peeling test in dimension one (2016). SISSA Preprint, Trieste

    Google Scholar 

  21. Dal Maso, G., Zanini, C.: Quasi-static crack growth for a cohesive zone model with prescribed crack path. Proc. Roy. Soc. Edinb. Sect. A 137(2), 253–279 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  22. Dugdale, D.: Yielding of steel sheets containing clits. J. Mech. Phys. Solids 8, 100–104 (1960)

    Article  Google Scholar 

  23. Francfort, G.A., Marigo, J.J.: Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46(8), 1319–1342 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  24. Freddi, F., Iurlano, F.: Numerical insight of a variational smeared approach to cohesive fracture. J. Mech. Phys. Solids 98, 156–171 (2017)

    Article  MathSciNet  Google Scholar 

  25. Frémond, M.: Contact with adhesion. In: Moreau, J., Panagiotopoulos, P., Strang, G. (eds.) Topics in Nonsmooth Mechanics, pp. 157–186. Birkhäuser (1988)

    Google Scholar 

  26. Frémond, M.: Non-Smooth Thermomechanics. Springer, Heidelberg (2002)

    Book  MATH  Google Scholar 

  27. Giacomini, A.: Ambrosio-Tortorelli approximation of quasi-static evolution of brittle fracture. Calc. Var. Partial Differential Equations 22, 129–172 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  28. Giacomini, A., Ponsiglione, M.: Discontinuous finite element approximation of quasistatic crack growth in finite elasticity. Math. Models Methods Appl. Sci. 16(1), 77–118 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  29. Halphen, B., Nguyen, Q.: Sur les matériaux standards généralisés. J. Mécanique 14, 39–63 (1975)

    MathSciNet  MATH  Google Scholar 

  30. Keip, M.A., Kiefer, B., Schröder, J., Linder, C. (eds.): Special issue on phase field approaches to fracture: in memory of Professor Christian Miehe (19562016). Comput. Methods Appl. Mech. Eng. 312 (2016)

    Google Scholar 

  31. Kočvara, M., Mielke, A., Roubíček, T.: A rate-independent approach to the delamination problem. Math. Mech. Solids 11, 423–447 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  32. Lazzaroni, G., Rossi, R., Thomas, M., Toader, R.: Rate-independent damage in thermo-viscoelastic materials with inertia (2014). WIAS Preprint 2025

    Google Scholar 

  33. Marigo, J., Maurini, C., Pham, K.: An overview of the modelling of fracture by gradient damage models. Meccanica 51(12), 3107–3128 (2016)

    Article  MathSciNet  Google Scholar 

  34. Miehe, C., Hofacker, M., Welschinger, F.: A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits. Comput. Methods Appl. Mech. Eng. (2010)

    Google Scholar 

  35. Miehe, C., Welschinger, F., Hofacker, M.: Thermodynamically consistent phase-field models of fracture: variational principles and multi-field FE implementations. Int. J. Numer. Meth. Engng. 83, 12731311 (2010)

    MathSciNet  MATH  Google Scholar 

  36. Mielke, A.: Evolution in rate-independent systems (Chap. 6). In: C. Dafermos, E. Feireisl (eds.) Handbook of Differential Equations, Evolutionary Equations, vol. 2, pp. 461–559. Elsevier B.V., Amsterdam (2005)

    Google Scholar 

  37. Mielke, A., Roubíček, T.: Rate-Independent Systems: Theory and Application. Applied Mathematical Sciences. Springer, New York (2015)

    Book  MATH  Google Scholar 

  38. Mielke, A., Theil, F.: On rate-independent hysteresis models. NoDEA Nonlinear Differential Equations Appl. 11(2), 151–189 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  39. Mielke, A., Theil, F., Levitas, V.I.: A variational formulation of rate-independent phase transformations using an extremum principle. Arch. Ration. Mech. Anal. 162, 137–177 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  40. Ohtsuka, K.: Comparison of criteria on the direction of crack extension. J. Comput. Appl. Math. 149, 335–339 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  41. Ortiz, M., Pandolfi, A.: Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int. J. Numer. Meth. Eng. 44, 1267–1282 (1999)

    Article  MATH  Google Scholar 

  42. Rice, J.: Fracture, Chapter Mathematical Analysis in the Mechanics of Fracture, pp. 191–311. Academic Press, New York (1968)

    Google Scholar 

  43. Rossi, R., Roubíček, T.: Thermodynamics and analysis of rate-independent adhesive contact at small strains. Nonlinear Anal. 74(10), 3159–3190 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  44. Rossi, R., Roubíček, T.: Adhesive contact delaminating at mixed mode, its thermodynamics and analysis. Interfaces Free Bound. 15(1), 1–37 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  45. Rossi, R., Thomas, M.: From an adhesive to a brittle delamination model in thermo-visco-elasticity. ESAIM Control Optim. Calc. Var. 21, 1–59 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  46. Rossi, R., Thomas, M.: From adhesive to brittle delamination in visco-elastodynamics. WIAS-Preprint 2259 (2016)

    Google Scholar 

  47. Rossi, R., Thomas, M.: Coupling rate-independent and rate-dependent processes: existence results. WIAS-Preprint 2123. SIMA, accepted (2017)

    Google Scholar 

  48. Roubíček, T.: Rate-independent processes in viscous solids at small strains. Math. Methods Appl. Sci. 32(7), 825–862 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  49. Roubíček, T., Scardia, L., Zanini, C.: Quasistatic delamination problem. Continuum Mech. Thermodynam. 21(3), 223–235 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  50. Roubíček, T., Thomas, M., Panagiotopoulos, C.: Stress-driven local-solution approach to quasistatic brittle delamination. Nonlinear Anal. Real World Appl. 22, 645–663 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  51. Scala, R.: A weak formulation for a rate-independent delamination evolution with inertial and viscosity effects subjected to unilateral constraint. WIAS-Preprint 2172 (2015)

    Google Scholar 

  52. Scala, R.: Limit of viscous dynamic processes in delamination as the viscosity and inertia vanish. ESAIM COCV 23, 593–625 (2017)

    Google Scholar 

  53. Scala, R., Schimperna, G.: A contact problem for viscoelastic bodies with inertial effects and unilateral boundary constraints,. WIAS-Preprint 2147 (2015)

    Google Scholar 

  54. Schlüter, A., Willenbächer, A., Kuhn, C., Müller, R.: Phase field approximation of dynamic brittle fracture. Comput. Mech. 54, 1141–1161 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  55. Takaishi, T., Kimura, M.: Phase field model for mode III crack growth in two dimensional elasticity. Kybernetika 45(4), 605–614 (2009)

    MathSciNet  MATH  Google Scholar 

  56. Thomas, M., Mielke, A.: Damage of nonlinearly elastic materials at small strain: existence and regularity results. Zeit. Angew. Math. Mech. 90(2), 88–112 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  57. Thomas, M., Zanini, C.: Cohesive zone-type delamination in visco-elasticity. WIAS-preprint 2350 (2016)

    Google Scholar 

  58. Watanabe, K., Azegami, H.: Proposal of new stability-instability criterion for crack extension based on crack energy density and physical sytematization of other criteria. Bull. JSME 28(246), 2873–2880 (1985)

    Article  Google Scholar 

  59. Weinberg, K., Dally, T., Schuß, S., Werner, M., Bilgen, C.: Modeling and numerical simulation of crack growth and damage with a phase field approach. GAMM-Mitt. 39(1), 55–77 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The research of the author has been partially funded by the DFG (German Research Foundation) within Project Finite element approximation of functions of bounded variation and application to models of damage, fracture, and plasticity of the DFG Priority Programme SPP 1748 Reliable Simulation Techniques in Solid Mechanics. Development of Non-standard Discretisation Methods, Mechanical and Mathematical Analysis. This work was composed in the course of the International Conference CoMFoS16 Mathematical Analysis of Continuum Mechanics and Industrial Applications II held 2016 October 22th–24th at Kyushu University, Fukuoka, Japan. The author warmly thanks the organizing committee and, in particular, the organizers Masato Kimura, Patrick van Meurs, and Hirofumi Notsu (all Kanazawa University) for the invitation to the conference and for their hospitality at this successful event.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marita Thomas .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Thomas, M. (2018). A Comparison of Delamination Models: Modeling, Properties, and Applications. In: van Meurs, P., Kimura, M., Notsu, H. (eds) Mathematical Analysis of Continuum Mechanics and Industrial Applications II. CoMFoS 2016. Mathematics for Industry, vol 30. Springer, Singapore. https://doi.org/10.1007/978-981-10-6283-4_3

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-6283-4_3

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-6282-7

  • Online ISBN: 978-981-10-6283-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics