A quasi-static rate-independent model of delamination of linearly elastic bodies at small strains, sensitive to mode of delamination, using interfacial damage and interfacial plasticity as two internal parameters, is further developed with the aim to extract representations typically employed in engineering interface-models, i.e. fracture envelope and fracture energy dependence on the mode mixity, which are suitable for the model fitting to experimental data. Moreover, two concepts of solutions are implemented: globally stable energy-conserving solutions or stress-driven maximally-dissipative local solutions, arising by the fully implicit or by a semi-implicit time-stepping procedures, respectively, both yielding numerically stable and convergent time-discretizations. Spatial discretization is performed by the symmetric Galerkin boundary-element method (SGBEM). Alternating quadratic programming is implemented to cope with, respectively, global or local, energy-minimizations in the computation of the time-discretized solutions. Sample 2D numerical examples document applicability of the model as well as efficiency of the SGBEM numerical implementation and facilitate comparison of the two mentioned solution concepts.
This is a preview of subscription content, log in to check access.
The authors are indebted to an anonymous reviewer for many useful suggestions that improved the presentation in particular aspects. A part of the work has been accomplished during the stages of R. V. and T. R. at Universidad de Sevilla whose hospitality is acknowledged. Moreover, the authors acknowledge the support from the Spanish Ministry of Education (Ref. SAB2010-0082) and Spanish Ministry of Economy and Competitiveness (Project MAT2012-37387), from the Junta de Andalucía and European Social Fund through the Project of Excellence P08-TEP-04051, from the Slovak Ministry of Education through the grant 1/0201/11 (VEGA), as well as from the Czech Republic through the grants 201/10/0357, 201/12/0671, and 105/13/18652S (GA ČR), together with the institutional support RVO: 61388998.
Kolluri M, Hoefnagels JPM, van Dommelen JAW, Geers MGD (2011) An improved miniature mixed-mode delamination setup for in situ microscopic interface failure analyses. J Phys D Appl Phys 44:034005Google Scholar
Kolluri M, Hoefnagels JPM, van Dommelen JAW, Geers MGD (2013) A practical approach for the separation of interfacial toughness and structural plasticity in a delamination growth experiment. Int J Fract 183:1–18CrossRefGoogle Scholar
Liechti K, Chai Y (1992) Asymmetric shielding in interfacial fracture under in-plane sheare. J Appl Mech 59:295–304CrossRefGoogle Scholar
Mantič V (2008) Discussion on the reference length and mode mixity for a bimaterial interface. J Eng Mater Technol 130:045501-1-2Google Scholar
Mantič V, Távara L, Blázquez A, Graciani E, París F (2013) Application of a linear elastic–brittle interface model to the crack initiation and propagation at fibre–matrix interface under biaxial transverse loads. ArXiv preprint. arXiv:1311.4596.
Matzenmiller A, Gerlach S, Fiolka M (2010) A critical analysis of interface constitutive models for the simulation of delamination in composites and failure of adhesive bonds. J Mech Mater Struct 5:185–211CrossRefGoogle Scholar
Mielke A (2011) Differential, energetic and metric formulations for rate-independent processes. In: Ambrosio L, Savaré G (eds) Nonlinear PDEs and applications. Springer, Heidelberg, pp 87–170Google Scholar
Mielke A, Roubíček T (2015) Rate-independent systems—theory and application. Applied Mathematical Sciences Series. Springer, New York (contracted)Google Scholar
Mielke A, Roubíček T, Zeman J (2010) Complete damage in elastic and viscoelastic media and its energetics. Comput Methods Appl Mech Eng 199:1242–1253CrossRefMATHADSGoogle Scholar
Moreo P, García-Aznar JM, Doblaré M (2007) A coupled viscoplastic rate-dependent damage model for the simulation of fatigue failure of cement-bone interfaces. Int J Plasticity 23:2058–2084CrossRefMATHGoogle Scholar
Panagiotopoulos CG, Mantič V, Roubíček T (2013) BEM implementation of energetic solutions for quasistatic delamination problems. Comput Mech 51:505–521MathSciNetCrossRefMATHGoogle Scholar
París F, Cañas J (1997) Boundary element method. Fundamentals and applications. Oxford University Press, OxfordMATHGoogle Scholar
Roubíček T, Panagiotopoulos C, Mantič V (2013) Quasistatic adhesive contact of visco-elastic bodies and its numerical treatment for very small viscosity. Z Angew Math Mech 93:823–840CrossRefMATHGoogle Scholar
Roubíček T, Kružík M, Zeman J (2014) Delamination and adhesive contact models and their mathematical analysis and numerical treatment. In: Mantič V (ed) Mathematical methods and models in composites. Imperial College Press, London, pp 349–400Google Scholar
Roubíček T, Panagiotopoulos C, Mantič V (submitted) Local-solution approach to quasistatic rate-independent mixed-mode delamination. Math Models Methods Appl SciGoogle Scholar
Sauter SA, Schwab C (2010) Boundary element methods. Springer, BerlinGoogle Scholar
Scheider I (2009) Derivation of separation laws for cohesive models in the course of ductile fracture. Eng Fract Mech 76:1450–1459CrossRefGoogle Scholar
Scheider I, Mosler J (2011) Novel approach for the treatment of cyclic loading using a potential-based cohesive zone model. Procedia Eng 10:2164–2169CrossRefGoogle Scholar
Sirtori S (1979) General stress analysis by means of integral equations and boundary elements. Meccanica 14:210–218CrossRefMATHGoogle Scholar
Sirtori S, Miccoli S, Korach E (1993) Symmetric coupling of finite elements and boundary elements. In: Kane JH, Maier G, Tosaka N, Atluri SN (eds) Advances in boundary element techniques. Springer, Berlin, pp 407–427Google Scholar
Snozzi L, Molinari J-F (2013) A cohesive element model for mixed mode loading with frictional contact capability. Int J Numer Methods Eng 93:510–526MathSciNetCrossRefGoogle Scholar
Spada A, Giambanco G, Rizzo P (2009) Damage and plasticity at the interfaces in composite materials and structures. Comput Methods Appl Mech Eng 198:3884–3901MathSciNetCrossRefMATHADSGoogle Scholar
Sutradhar A, Paulino GH, Gray LJ (2008) The symmetric Galerkin boundary element method. Springer, BerlinGoogle Scholar
Swadener J, Liechti K, deLozanne A (1999) The intrinsic toughness and adhesion mechanism of a glass/epoxy interface. J Mech Phys Solids 47:223–258CrossRefMATHADSGoogle Scholar
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 Bound Elem 35:207–222MathSciNetCrossRefMATHGoogle Scholar
Toader R, Zanini C (2009) An artificial viscosity approach to quasistatic crack growth. Boll Unione Matem Ital 2:1–36MathSciNetMATHGoogle Scholar
Vodička R, Mantič V, París F (2007) Symmetric variational formulation of BIE for domain decomposition problems in elasticity—an SGBEM approach for nonconforming discretizations of curved interfaces. CMES Comput Model Eng 17:173–203MATHGoogle Scholar
Vodička R, Mantič V, París F (2011) Two variational formulations for elastic domain decomposition problems solved by SGBEM enforcing coupling conditions in a weak form. Eng Anal Bound Elem 35:148–155MathSciNetCrossRefMATHGoogle Scholar
Xu Q, Lu Z (2013) An elastic–plastic cohesive zone model for metal-ceramic interfaces at finite deformations. Int J Plasticity 41:147–164CrossRefGoogle Scholar
Ziegler H (1958) An attempt to generalize Onsager’s principle, and its significance for rheological problems. Z Angew Math Phys 9b:748–763CrossRefMATHGoogle Scholar