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**Debonding of FRP and thin films from an elastic half-plane using a coupled FE-BIE model.**
*(English)*
Zbl 1403.74239

Summary: A Finite Element-Boundary Integral Equation (FE-BIE) coupling method is proposed to investigate a flexible bar weakly attached to an elastic orthotropic half-plane. Firstly, the analysis focused on the case of a bar subjected to horizontal forces and thermal loads considering interfacial displacements linearly proportional to the tangential traction. Secondly, the debonding behaviour of a composite reinforcement glued to a substrate has been modelled. Using an incremental nonlinear analysis, a bilinear elastic-softening interfacial traction-slip law has been implemented simulating the delamination of pure mode II. Finally, the influence of the anchorage length on the ultimate bearing capacity of the adhesive joint has been investigated.

### MSC:

74S15 | Boundary element methods applied to problems in solid mechanics |

74S05 | Finite element methods applied to problems in solid mechanics |

65N38 | Boundary element methods for boundary value problems involving PDEs |

74K35 | Thin films |

### Keywords:

mixed variational principle; Green function; weak interface; debonding; FRP-strengthening concrete
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\textit{E. Tezzon} et al., Eng. Anal. Bound. Elem. 93, 21--28 (2018; Zbl 1403.74239)

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### References:

[1] | Bakis, C; Bank, L; Brown, V; Cosenza, E; Davalos, J; Lesko, J; Machida, A; Rizkalla, S; Triantafillou, T, Fiber-reinforced polymer composites for construction - state of the art review, J Compos Constr, 6, 2, 73-87, (2002) |

[2] | Zhao X, L; Zhang, L, State of the art review on FRP strengthened steel structures, Eng Struct, 29, 8, 1808-1823, (2007) |

[3] | Teng, JG; Chen, JF; Smith, ST; Lam, L, FRP strengthened RC structures, (2001), John Wiley & Sons Chichester |

[4] | Grigolyuk, EI; Tolkachev, VM, Contact problems in the theory of plates and shells, (1987), Mir Publishers Moscow |

[5] | Lanzoni, L, Analysis of stress singularities in thin coatings bonded to a semi-infinite elastic substrate, Int J Solids Struct, 48, 13, 1915-1926, (2011) |

[6] | Lenci, S, Melan’s problems with weak interface, J Appl Mech Trans ASME, 67, 1, 22-28, (2000) · Zbl 1110.74546 |

[7] | Goland, M; Reissner, E, The stresses in cemented joints, J Appl Mech Trans ASME, 11, A17-A27, (1944) |

[8] | Geymonat, G; Krasucki, F; Lenci, S, Mathematical analysis of a bonded joint with soft thin adhesive, Math Mech Solids, 4, 2, 201-225, (1999) · Zbl 1001.74591 |

[9] | Rizzoni, R; Dumont, S; Lebon, F; Sacco, E, Higher order model for soft and hard elastic interfaces, Int J Solids Struct, 51, 1, 4137-4148, (2014) |

[10] | Caggiano, A; Martinelli, E; Faella, C, A fully-analytical approach for modelling the response of FRP plates bonded to a brittle substrate, Int J Solids Struct, 49, 17, 2291-2300, (2012) |

[11] | Franco, A; Royer-Carfagni, G, Cohesive debonding of a stiffener from an elastic substrate, Compos Struct, 111, 401-414, (2014) |

[12] | Franco, A; Royer-Carfagni, G, Effective bond length of FRP stiffeners, Int J Non-Linear Mech, 60, 46-57, (2014) |

[13] | Rabinovitch, O, Fracture-mechanics failure criteria for RC beams strengthened with FRP strips-a simplified approach, Compos Struct, 64, 3-4, 479-492, (2004) |

[14] | Wu, Z; Yin, J, Fracturing behaviors of FRP-strengthened concrete structures, Eng Fract Mech, 70, 10, 1339-1355, (2003) |

[15] | Lu, XZ; Ye, LP; Teng, JG; Jiang, JJ, Meso-scale finite element model for FRP sheets/plates bonded to concrete, Eng Struct, 27, 4, 564-575, (2005) |

[16] | Benzarti, K; Freddi, F; Frémond, F, A damage model to predict the durability of bonded assemblies. part I: debonding behaviour of FRP strengthened concrete structures, Constr Build Mater, 25, 2, 547-555, (2011) |

[17] | Benvenuti, E; Vitarelli, O; Tralli, A, Delamination of FRP-reinforced concrete by means of an extended finite element formulation, Compos Part B Eng, 43, 8, 3258-3269, (2012) |

[18] | Benvenuti, E; Ventura, G; Ponara, N; Tralli, A, Variationally consistent extended FE model for 3D planar and curved imperfect interfaces, Comput Method Appl Mech Eng, 267, 434-457, (2013) · Zbl 1286.74095 |

[19] | Benvenuti, E; Orlando, N; Ferretti, D; Tralli, A, A new 3D experimentally consistent XFEM to simulate delamination in FRP-reinforced concrete, Compos Part B Eng, 91, 346-360, (2016) |

[20] | Benvenuti, E; Orlando, N, Failure of FRP-strengthened SFRC beams through an effective mechanism-based regularized XFEM framework, Compos Struct, 172, 345-358, (2017) |

[21] | Zhang, Y-M; Gu, Y; Chen, J-T, Internal stress analysis for single and multilayered coating systems using the boundary element method, Eng Anal Bound Elem, 35, 4, 708-717, (2011) · Zbl 1259.74076 |

[22] | Zhang, Y; Li, X; Sladek, V; Sladek, J; Gao, X, A new method for numerical evaluation of nearly singular integrals over high-order geometry elements in 3D BEM, J Comput Appl Math, 277, 57-72, (2015) · Zbl 1302.65264 |

[23] | Zhang, Y-M; Qu, W-Z; Chen, J-T, BEM analysis of thin structures for thermoelastic problems, Eng Anal Bound Elem, 37, 2, 441-452, (2013) · Zbl 1351.74150 |

[24] | Gu, Y; Chen, W; Zhang, B, Stress analysis for two-dimensional thin structural problems using the meshless singular boundary method, Eng Anal Bound Elem, 59, 1-7, (2015) · Zbl 1403.74057 |

[25] | Salvadori, A, A symmetric boundary integral formulation for cohesive interface problems, Comput Mech, 32, 4-6, 381-391, (2003) · Zbl 1038.74668 |

[26] | Freddi, F; Savoia, M, Analysis of FRP-concrete debonding via boundary integral equations, Eng Fract Mech, 75, 6, 1666-1683, (2008) |

[27] | Tullini, N; Tralli, A; Lanzoni, L, Interfacial shear stress analysis of bar and thin film bonded to 2D elastic substrate using a couple FE-BIE method, Finite Elem Anal Des, 55, 42-45, (2012) |

[28] | Szabó, B; Babuška, I, Finite element analysis, (1991), John Wiley & Sons New York |

[29] | Tullini, N; Tralli, A, Static analysis of Timoshenko beam resting on elastic half-plane based on the coupling of locking-free finite elements and boundary integral, Comput Mech, 45, 2-3, 211-225, (2010) · Zbl 1271.74271 |

[30] | Baraldi, D; Tullini, N, Incremental analysis of elasto-plastic beams and frames resting on an elastic half-plane, J Eng Mech, 134, 9, 1-9, (2017), Article number 04017101 |

[31] | Tezzon, E; Tullini, N; Minghini, M, Static analysis of shear flexible beams and frames in adhesive contact with an isotropic elastic half-plane using a coupled FE-BIE model, Eng Struct, 104, 32-50, (2015) |

[32] | Tezzon, E; Tullini, N; Lanzoni, L, A coupled FE-BIE model for the static analysis of Timoshenko beams bonded to an orthotropic elastic half-plane, Eng Anal Bound Elem, 71, 112-128, (2016) · Zbl 1403.74240 |

[33] | Tullini, N; Tralli, A; Baraldi, D, Stability of slender beams and frames resting on 2D elastic half-space, Arch Appl Mech, 83, 3, 467-482, (2013) · Zbl 1293.74131 |

[34] | Tullini, N; Tralli, A; Baraldi, D, Buckling of Timoshenko beams in frictionless contact with an elastic half-plane, J Eng Mech, 139, 7, 824-831, (2013) |

[35] | Kikuchi, N; Oden, J, Contact problems in elasticity: a study of variational inequalities and finite element methods, (1988), SIAM Philadelphia · Zbl 0685.73002 |

[36] | Bielak, J; Stephan, E, A modified Galerkin procedure for bending of beams on elastic foundations, SIAM J Sci Stat Comput, 4, 2, 340-352, (1983) · Zbl 0541.73089 |

[37] | Ferracuti, B; Mazzotti, C; Savoia, M, A new single-shear set-up for stable debonding of FRP-concrete joints, Constr Build Mater, 23, 4, 1529-1537, (2008) |

[38] | Panigrahi, S; Pradhan, B, Onset and growth of adhesion failure and delamination induced damages in double lap joint of laminated FRP composites, Compos Struct, 85, 4, 326-336, (2008) |

[39] | Czaderski, C; Soudki, K; Motavalli, M, Front and side view image correlation measurements on FRP to concrete pull-off bond tests, J Compos Constr, 14, 4, 451-464, (2010) |

[40] | Martinelli, E; Czaderski, C; Motavalli, M, Modeling in-plane and out-of-plane displacement fields in pull-off tests on FRP strips, Eng Struct, 33, 12, 3715-3725, (2011) |

[41] | Johnson, KL, Contact mechanics, (1985), University Press Cambridge |

[42] | Gurtin, ME; Sternberg, E, Theorems in linear elastostatics for exterior domains, Arch Ration Mech Anal, 8, 1, 99-119, (1961) · Zbl 0101.17001 |

[43] | Yao, J; Teng, JG; Chen, JF, Experimental study on FRP to concrete bonded joints, Compos Part B Eng, 36, 2, 99-113, (2005) |

[44] | Taljsten, B, Defining anchor lengths of steel and CFRP plates bonded to concrete, Int J Adhes Adhes, 17, 4, 319-327, (1997) |

[45] | Lu, XZ; Teng, JG; Ye, LP; Jiang, JJ, Bond-slip models for FRP sheets/plates bonded to concrete, Eng Struct, 27, 920-937, (2005) |

[46] | Faella, C; Martinelli, E; Nigro, E, Direct versus indirect method for identifying FRP to concrete interface relationships, J Compos Constr, 13, 3, 226-233, (2009) |

[47] | Chajes, MJ; Finch, WW; Januska, TF; Thomson, TA, Bond and force transfer of composite material plates bonded to concrete, ACI Struct J, 93, 2, 208-217, (1996) |

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