Towards nonlinear imperfect interface models including micro-cracks and smooth roughness

Annals of Solid and Structural Mechanics - Tập 9 Số 1-2 - Trang 13-27 - 2017
Serge Dumont1, Frédéric Lebon2, Maria Letizia Raffa3, Raffaella Rizzoni4
1Université de Nîmes, Institut Montpellierain Alexander Grothendieck, CNRS UMR 5149, CC 051, Place Eugène Bataillon, 34090, Montpellier, France
2Aix-Marseille Univ, CNRS, Centrale Marseille, LMA, Marseille, France
3CNRS, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 61 avenue du Général de Gaulle, 94010, Créteil Cedex, France
4Department of Engineering, University of Ferrara, Via Saragat 1, 44122 Ferrara, Italy

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Tài liệu tham khảo

Becker R, Hansbo P, Stenberg R (2010) A finite element method for domain decomposition with non-matching grids. ESAIM M2AN 37(2):209–225

Benveniste Y, Miloh T (2001) Imperfect soft and stiff interfaces in two-dimensional elasticity. Mech Mater 33(6):309–323

Bonetti E, Bonfanti G, Lebon F, Rizzoni R (2017) A model of imperfect interface with damage. Meccanica (in press)

Bornert PG, Bretheau T, Gilormini P (2001) Homogénéisation en mécanique des matériaux, Tome 1: Matériaux aléatoires élastiques et milieux périodiques. Hermes Sciences, Paris

Challamel N, Girhammar UA (2011) Boundary-layer effect in composite beams with interlayer slip. J Aerosp Eng 24(2):199–209

Ciarlet PG (1988) Mathematical elasticity: three-dimensional elasticity, vol 1. North-Holland

Dacorogna B (2008) Direct methods in the calculus of variations. Appl Math Sci 78. Springer, New York

Dumont S, Goubet O, Ha-Duong T, Villon P (2006) Meshfree methods and boundary conditions. Int J Numer Meth Eng 67:989–1011

Dumont S, Lebon F, Rizzoni R (2014) An asymptotic approach to the adhesion of thin stiff films. Mech Res Com 58:24–35

Dacorogna B, Marcellini P (1995) Existence of minimizers for non-quasiconvex integrals. Arch Ration Mech Anal 131:359–399

Fouchal F, Lebon F, Raffa ML, Vairo G (2014) An interface model including cracks and roughness applied to masonry. Open Civ Eng J 8:263–271

Geymonat G, Krasucki F, Lenci S (1999) Mathematical analysis of a bonded joint with a soft thin adhesive. Math Mech Sol 4(2):201–225

Hashin Z (2002) Thin interphase/imperfect interface in elasticity with application to coated fiber composites. J Mech Phys Solids 50(12):2509–2537

Ivanov IV, Velchev DS, Kneć M, Sadowski T (2011) Computational models of laminated glass plate under transverse static loading. In: Altenbach H, Eremeyev VA (eds)“Shell-line structures”, non-classical theories and applications. Adv Struct Mat, Springer, Berlin, pp 469–490 (2011)

Klarbring A (1991) Derivation of the adhesively bonded joints by the asymptotic expansion method. Int J Eng Sci 29:493–512

Lebon F, Ould Khaoua A, Licht C (1998) Numerical study of soft adhesively bonded joints in finite elasticity. Comp Mech 21:134–140

Lebon F, Rizzoni R (2008) Asymptotic study on a soft thin layer: the non-convex case. Mech Adv Mat Struct 15:12–20

Lebon F, Rizzoni R (2010) Asymptotic analysis of a thin interface: the case involving similar rigidity. Int J Eng Sci 48:473–486

Lebon F, Rizzoni R (2011) Asymptotic behavior of a hard thin linear elastic interphase: an energy approach. Int J Sol Struct 48:441–449

Lebon F, Rizzoni R (2013) Modeling a hard, thin curvilinear interface. Discr Cont Dyn Syst Ser S 6(6):1569–1586

Lebon F, Rizzoni R, Ronel-Idrissi S (2004) Asymptotic analysis of some non-linear soft thin layers. Comp Struct 82:1929–1938

Lebon F, Ronel-Idrissi S (2004) Asymptotic analysis of Drucker–Prager and Mohr–Coulomb soft thin interfaces. Steel Comp Struct 4:133–147

Lebon F, Zaittouni S (2010) Asymptotic modelling of interfaces taking contact conditions into account: asymptotic expansions and numerical implementation. Int J Eng Sci 48:111–127

Le Dret H, Raoult A (1995) The quasiconvex envelope of the Saint Venant–Kirchhoff stored energy function. Proc R Soc Edinb 125A:1179–1192

Lenci S, Clementi F, Warminski J (2015) Nonlinear free dynamics of a two-layer composite beam with different boundary conditions. Meccanica 50(3):675–688

Li YD, Xiong T, Dong L (2015) A new interfacial imperfection coupling model (IICM) and its effect on the facture behavior of a layered multiferroic composite: anti-plane case. Eur J Mech A Solids 52:26–36

Li Z (1996) Existence of minimizers and microstructure in nonlinear elasticity. Nonlinear Anal Theor 27(3):297–308

Lopez-Realpozo JC, Rodriguez-Ramos R, Guinovart-Diaz R, Bravo-Castillero J, Otero JA, Sabina FJ, Lebon F, Dumont S, Sevostianov I (2014) Effective elastic shear stiffness of a periodic fibrous composite with non-uniform imperfect contact between the matrix and the fibers. Int J Solids Struct 51(6):1253–1262

Mardare C (2010) Existence of minimizers for the pure displacement problem in nonlinear elasticity, “Alexandru Myller” mathematical seminar. Romania 1329:181–190

Mauge C, Kachanov M (1994) Effective elastic properties of an anisotropic material with arbitrarily oriented interacting cracks. J Mech Phys Solids 42:561–584

Nairn JA (2007) Numerical implementation of imperfect interfaces. Comp Mat Sci 40:525–536

Nitsche J (1974) Convergence of nonconforming methods. In: Mathematical aspects of finite elements in partial differential equations. Proc. Sympos. Math. Res. Center, University of Wisconsin, Madison. Academic Press, New York, pp 15–53

Orifice A, Mancusi G, Dumont S, Lebon F (2016) An experimental/numerical study on the interfacial damage of bonded joints for fibre-reinforced polymer profiles at service conditions. Technologies. doi: 10.3390/technologies4030020

Pelissou C, Lebon F (2009) Asymptotic modeling of quasi-brittle interfaces. Comp Struct 87:1216–1223

Ponte Castaneda M, Willis J (1995) The effect of spatial distribution on the effective behavior of composite materials and cracked media. J Mech Phys Sol 43:1919–1951

Raffa ML, Lebon F, Rizzoni R (2016) On modelling brick/mortar interface via a St. Venant–Kirchhoff orthotropic soft interface. Part I: theory. Int J Mason Res Innov 1(2):142–164

Raffa ML, Lebon F, Vairo G (2016) Normal and tangential stiffnesses of rough surfaces in contact via an imperfect interface model. Int J Sol Struct 87:245–253

Raffa ML, Lebon F, Rizzoni R (2017) On modelling brick/mortar interface via a St. Venant–Kirchhoff orthotropic soft interface. Part II: in silico analysis. Int J Mason Res Innov (in press)

Raffa ML, Lebon F, Rizzoni R (2017) Derivation of a model of imperfect interface with finite strains and damage by asymptotic techniques. Application to masonry structures. Meccanica (in review)

Rekik A, Lebon F (2010) Identification of the representative crack length evolution in a multi-level interface model for quasi-brittle masonry. Int J Solids Struct 47(22–23):3011–3021

Rekik A, Lebon F (2012) Homogenization methods for interface modeling in damaged masonry. Adv Eng Softw 46(1):35–42

Rizzoni R, Lebon F (2012) Asymptotic analysis of an adhesive joint with mismatch strain. Eur J Mech A Sol 36:1–8

Rizzoni R, Lebon F (2013) Imperfect interfaces as asymptotic models of thin curved elastic adhesive interphases. Mech Res Comm 51:39–50

Rizzoni R, Dumont S, Lebon F (2015) On Saint Venant–Kirchhoff imperfect interfaces. Int J Non-Linear Mech 89:101–115

Rizzoni R, Dumont S, Lebon F, Sacco S (2014) Higher order model for soft and hard elastic interfaces. Int J Solids Struct 51:4137–4148

Serpilli M (2014) Asymptotic analysis of a multimaterial with a thin piezoelectric interphase. Meccanica 49(7):1641–1652

Stenberg R (1995) On some techniques for approximating boundary conditions in the finite element method. J Comput Appl Math 63:139–148

Tsukrov I, Kachanov M (2000) Effective moduli of an anisotropic material with elliptical holes of arbitrary orientational distribution. Int J Solids Struct 37(41):5919–5941