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BEM solution of delamination problems using an interface damage and plasticity model

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Abstract

The problem of quasistatic and rate-independent evolution of elastic-plastic-brittle delamination at small strains is considered. Delamination processes for linear elastic bodies glued by an adhesive to each other or to a rigid outer surface are studied. The energy amounts dissipated in fracture Mode I (opening) and Mode II (shear) at an interface may be different. A concept of internal parameters is used here on the delaminating interfaces, involving a couple of scalar damage variable and a plastic tangential slip with kinematic-type hardening. The so-called energetic solution concept is employed. An inelastic process at an interface is devised in such a way that the dissipated energy depends only on the rates of internal parameters and therefore the model is associative. A fully implicit time discretization is combined with a spatial discretization of elastic bodies by the BEM to solve the delamination problem. The BEM is used in the solution of the respective boundary value problems, for each subdomain separately, to compute the corresponding total potential energy. Sample problems are analysed by a collocation BEM code to illustrate the capabilities of the numerical procedure developed.

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References

  1. Banks-Sills L, Ashkenazi D (2000) A note on fracture criteria for interface fracture. Int J Frac 103:177–188

    Article  Google Scholar 

  2. Bažant Z, Jirásek M (2002) Nonlocal integral formulations of plasticity and damage: survey of progress. J Eng Mech 128(11):1119–1149

    Article  Google Scholar 

  3. Benešová B (2009) Modeling of shape-memory alloys on the mesoscopic level. In: Šittner P et al. (ed) Proc. ESOMAT 2009, EDP Sciences, 03003, pp 1–7

  4. Benešová B (2011) Global optimization numerical strategies for rate-independent processes. J Global Optim 50:197–220

    Article  MathSciNet  MATH  Google Scholar 

  5. Biot MA (1956) Thermoelasticity and irreversible thermodynamics. J Appl Phys 27:240–253

    Article  MathSciNet  MATH  Google Scholar 

  6. Biot MA (1965) Mechanics of incremental deformations. Wiley, New York

    Google Scholar 

  7. Bourdin B, Francfort GA, Marigo JJ (2000) Numerical experiments in revisited brittle fracture. J Mech Phys Solids 48:797–826

    Article  MathSciNet  MATH  Google Scholar 

  8. Byrd RH, Lu P, Nocedal J, Zhu C (1994) A limited memory algorithm for bound constrained optimization. SIAM J Sci Comput 16:1190–1208

    Article  MathSciNet  Google Scholar 

  9. Carpinteri A, Cornetti P, Pugno N (2009) Edge debonding in FRP strengthened beams: stress versus energy failure criteria. Eng Struct 31:2436–2447

    Article  Google Scholar 

  10. Cornetti P, Carpinteri A (2011) Modelling the FRP-concrete delamination by means of an exponential softening law. Eng Struct 33:1988–2001

    Article  Google Scholar 

  11. Dostál Z (2009) Optimal quadratic programming algorithms: with applications to variational inequalities. Springer, New York

    MATH  Google Scholar 

  12. Evans A, Rühle M, Dalgleish B, Charalambides P (1990) The fracture energy of bimaterial interfaces. Metall Trans A 21A: 2419–2429

    Google Scholar 

  13. Figueiredo MAT, Nowak RD, Wright SJ (2008) Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J Selected Topics Signal Process 1:586–597

    Article  Google Scholar 

  14. Frémond M (1985) Dissipation dans l’adherence des solides. C.R. Acad Sci, Paris, Sér.II 300(15):709–714

  15. Griffith A (1921) The phenomena of rupture and flow in solids. Philos Trans Royal Soc London Ser A Math Phys Eng Sci 221:163–198

    Article  Google Scholar 

  16. Han W, Reddy BD (1999) Plasticity: Mathematical theory and numerical analysis. Springer, New York

    MATH  Google Scholar 

  17. Hartmann F (1989) Introduction to boundary elements theory and applications. Springer, Berlin

    Book  MATH  Google Scholar 

  18. Hui CY, Ruina A, Long R, Jagota A (2011) Cohesive zone models and fracture. J Adhes 87:1–52

    Article  Google Scholar 

  19. Hutchinson JW, Suo Z (1992) Mixed mode cracking in layered materials. Adv Appl Mech 29:63–191

    Article  MATH  Google Scholar 

  20. Khoromskij BN, Wittum G (2004) Numerical solution of elliptic differential equations by reduction to the interface. Springer, Berlin

    Book  MATH  Google Scholar 

  21. Kolluri M, Thissen M, Hoefnagels J, van Dommelen J, Geers M (2009) In-situ characterization of interface delamination by a new miniature mixed mode bending setup. Int J Fract 158:183–195

    Article  MATH  Google Scholar 

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

    Google Scholar 

  23. Lenci A (2001) Analysis of a crack at a weak interface. Int J Fract 108:275–290

    Article  Google Scholar 

  24. Liechti K, Chai Y (1992) Asymmetric shielding in interfacial fracture under in-plane shear. J Appl Mech 59:295–304

    Article  Google Scholar 

  25. Makhorin A (2004) GLPK-GNU linear programming Kit. Free Software Foundation, version 4.4

  26. Mantič V (1993) A new formula for the C-matrix in the Somigliana identity. J Elast 33:191–201

    Article  MATH  Google Scholar 

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

  28. Mielke A (2010) Differential, energetic and metric formulations for rate-independent processes. In: Ambrosio L, Savaré G (eds) Nonlinear PDEs and applications. Springer, New York, pp 87–170

  29. Mielke A, Roubíček T (2006) Rate-independent damage processes in nonlinear elasticity. Math Models Meth Appl Sci 16:177–209

    Article  MATH  Google Scholar 

  30. Mielke A, Roubíček T (2009) Numerical approaches to rate-independent processes and applications in inelasticity. Math Model Numer Anal (M2AN) 43, 399–428

    Google Scholar 

  31. Mielke A, Roubíček T, Zeman J (2009) Complete damage in elastic and viscoelastic media and its energetics. Comput Methods Appl Mech Eng 199:1242–1253

    Article  Google Scholar 

  32. Mielke A, Theil F (2001) On rate-independent hysteresis models. Nonl Diff Eqns Appl (NoDEA) 11:151–189

    MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  34. Panagiotopoulos CG (2010) Open BEM project. http://www.openbemproject.org/

  35. París F, Cañas J (1997) Boundary element method fundamentals and applications. Oxford University Press, Oxford

    MATH  Google Scholar 

  36. Roubíček T, Kružík M, Zeman J (2013) Delamination and adhesive contact models and their mathematical analysis and numerical treatment. In: Mantič V, (ed) Math. Methods & Models in Composites, chap. 9. Imperial College Press, London

  37. Roubíček T, Mantič V, Panagiotopoulos CG (2013) Quasistatic mixed-mode delamination model. Discrete and Continuous Dynamical Systems, Series S 6:591–610

    Google Scholar 

  38. Sauter SA, Schwab C (2010) Boundary element methods. Springer, Berlin

  39. Simo J, Hughes T (1998) Computational inelasticity. Springer, New York

  40. Távara L, Mantič V, Graciani E, Cañas J, París F (2010) Analysis of a crack in a thin adhesive layer between orthotropic materials: an application to composite interlaminar fracture toughness test. Comput Model Eng Sci (CMES) 58:247–270

    MATH  Google Scholar 

  41. Távara L, Mantič V, Graciani E, París F (2011) BEM analysis of crack onset and propagation along fiber-matrix interface under transverse tension using a linear elastic-brittle interface model. Eng Anal Boundary Elem 35:207–222

    Article  Google Scholar 

  42. Tvergaard V, Hutchinson J (1993) The influence of plasticity on mixed mode interface toughness. J Mech Phys Solids 41: 1119–1135

    Google Scholar 

  43. Vodička R, Mantič V (2011) An energetic approach to mixed mode delamination problem - an SGBEM implementation. In: Výpočty konstrukcí metodou konečných prvk\(\mathring{\rm u}\). ISBN 978-80-261-0059-1, Západočeská univerzita v Plzni, Plzeň

  44. Williams ML (1959) The stresses around a fault or crack in dissimilar media. Bull Seismol Soc Am 49:199–204

    Google Scholar 

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Acknowledgments

The support by the Junta de Andalucía and Fondo Social Europeo (Proyecto de Excelencia TEP-4051) is warmly acknowledged. VM also acknowledges the support by the Ministerio de Ciencia e Innovación (Proyecto MAT2009-14022). TR acknowledges partial support from the grants 201/09/0917, 201/10/0357, and 201/12/0671 (GA ČR), and the institutional support RVO: 67985971 (ČR).

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Authors and Affiliations

  1. Group of Elasticity and Strength of Materials, Department of Continuum Mechanics, School of Engineering, University of Seville, Camino de los Descubrimientos s/n, 410 92 , Sevilla, Spain

    C. G. Panagiotopoulos & V. Mantič

  2. Mathematical Institute, Charles University, Sokolovská 83, 18675 , Praha 8, Czech Republic

    T. Roubíček

  3. Institute of Thermomechanics of the ASCR, Dolejškova 5, 182 00 , Praha 8, Czech Republic

    T. Roubíček

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  1. C. G. Panagiotopoulos
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  2. V. Mantič
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  3. T. Roubíček
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Correspondence to C. G. Panagiotopoulos.

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Panagiotopoulos, C.G., Mantič, V. & Roubíček, T. BEM solution of delamination problems using an interface damage and plasticity model. Comput Mech 51, 505–521 (2013). https://doi.org/10.1007/s00466-012-0826-3

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