Cohesive delamination and frictional contact on joining surface via XFEM

Francesco Parrinello; Giuseppe Marannano; Francesco Parrinello; Giuseppe Marannano

doi:10.3934/matersci.2018.1.127

AIMS Materials Science

2018, Volume 5, Issue 1: 127-144. doi: 10.3934/matersci.2018.1.127

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Research article Topical Sections

Cohesive delamination and frictional contact on joining surface via XFEM

Francesco Parrinello ^{1
,
,},
Giuseppe Marannano ²

1.
Dipartimento di Ingegneria Civile Ambientale Aerospaziale e dei Materiali, Universitá of Palermo, Viale delle Scienza, 90128 Palermo, Italy
2.
Dipartimento di Ingegneria Innovazione Industriale e Digitale, Universitá of Palermo, Viale delle Scienza, 90128 Palermo, Italy

Received: 14 December 2017 Accepted: 13 February 2018 Published: 28 February 2018

In the present paper, the complex mechanical behaviour of the surfaces joining two different bodies is analysed by a cohesive-frictional interface constitutive model. The kinematical behaviour is characterized by the presence of discontinuous displacement fields, that take place at the internal connecting surfaces, both in the fully cohesive phase and in the delamination one. Generally, in order to catch discontinuous displacement fields, internal connecting surfaces (adhesive layers) are modelled by means of interface elements, which connect, node by node, the meshes of the joined bodies, requiring the mesh to be conforming to the geometry of the single bodies and to the relevant connecting surface. In the present paper, the Extended Finite Element Method (XFEM) is employed to model, both from the geometrical and from the kinematical point of view, the whole domain, including the connected bodies and the joining surface. The joining surface is not discretized by specific finite elements, but it is defined as an internal discontinuity surface, whose spatial position inside the mesh is analytically defined. The proposed approach is developed for two-dimensional composite domains, formed by two or more material portions joined together by means of a zero thickness adhesive layer. The numerical results obtained with the proposed approach are compared with the results of the classical interface finite element approach. Some examples of delamination and frictional contact are proposed with linear, circular and curvilinear adhesive layer.
- joined solids,
- interface,
- XFEM,
- cohesive-frictional,
- delamination
Citation: Francesco Parrinello, Giuseppe Marannano. Cohesive delamination and frictional contact on joining surface via XFEM[J]. AIMS Materials Science, 2018, 5(1): 127-144. doi: 10.3934/matersci.2018.1.127

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Abstract

In the present paper, the complex mechanical behaviour of the surfaces joining two different bodies is analysed by a cohesive-frictional interface constitutive model. The kinematical behaviour is characterized by the presence of discontinuous displacement fields, that take place at the internal connecting surfaces, both in the fully cohesive phase and in the delamination one. Generally, in order to catch discontinuous displacement fields, internal connecting surfaces (adhesive layers) are modelled by means of interface elements, which connect, node by node, the meshes of the joined bodies, requiring the mesh to be conforming to the geometry of the single bodies and to the relevant connecting surface. In the present paper, the Extended Finite Element Method (XFEM) is employed to model, both from the geometrical and from the kinematical point of view, the whole domain, including the connected bodies and the joining surface. The joining surface is not discretized by specific finite elements, but it is defined as an internal discontinuity surface, whose spatial position inside the mesh is analytically defined. The proposed approach is developed for two-dimensional composite domains, formed by two or more material portions joined together by means of a zero thickness adhesive layer. The numerical results obtained with the proposed approach are compared with the results of the classical interface finite element approach. Some examples of delamination and frictional contact are proposed with linear, circular and curvilinear adhesive layer.

References

[1]	Dugdale D (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8: 100–104. doi: 10.1016/0022-5096(60)90013-2
[2]	Barenblatt G (1962) The mathematical theory of equilibrium cracks in brittle fracture. Adv Appl Mech 7: 55–129. doi: 10.1016/S0065-2156(08)70121-2
[3]	Allix O, Blanchard L (2006) Mesomodeling of delamination: towards industrial applications. Compos Sci Technol 66: 731–744. doi: 10.1016/j.compscitech.2004.12.023
[4]	Allix O, Ladevéze P (1992) Interlaminar interface modeling for the prediction of delamination. Compos Struct 22: 235–242. doi: 10.1016/0263-8223(92)90060-P
[5]	Borino G, Fratini L, Parrinello F (2009) Mode I failure modeling of friction stir welding joints. Int J Adv Manuf Tech 41: 498–503. doi: 10.1007/s00170-008-1498-1
[6]	Corigliano A (1993) Formulation, identification and use of interface models in the numerical analysis of composite delamination. Int J Solids Struct 30: 2779–2811. doi: 10.1016/0020-7683(93)90154-Y
[7]	Mi Y, Crisfield MA, Davies GAO, et al. (1998) Progressive delamination using Interface elements. J Compos Mater 32: 1246–1272. doi: 10.1177/002199839803201401
[8]	Alfano G, Crisfield MA (2001) Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues. Int J Numer Meth Eng 50: 1701–1736. doi: 10.1002/nme.93
[9]	Qiu Y, Crisfield MA, Alfano G (2001) An interface element formulation for the simulation of delamination with buckling. Eng Fract Mech 68: 1755–1776. doi: 10.1016/S0013-7944(01)00052-2
[10]	Zou Z, Reid SR, Li S (2003) A continuum damage model for delamination in laminated composites. J Mech Phys Solids 51: 333–356. doi: 10.1016/S0022-5096(02)00075-3
[11]	Point N, Sacco E (1996) A delamination model for laminated composites. Int J Solids Struct 33: 483–509. doi: 10.1016/0020-7683(95)00043-A
[12]	Mortara G, Boulon M, Ghionna VN (2002) A 2-D constitutive model for cyclic interface behaviour. Int J Numer Anal Met 26: 1071–1096. doi: 10.1002/nag.236
[13]	Carol I, López CM, Roa O (2001) Micromechanical analysis of quasi-brittle materials using fracture-based interface elements. Int J Numer Meth Eng 52: 193–215. doi: 10.1002/nme.277
[14]	Cocchetti G, Maier G, Shen XP (2002) Piecewise linear models for interfaces and mixed mode cohesive cracks. CMES-Comp Model Eng 3: 279–298.
[15]	Tvergaard V (1990) Effect of fiber debonding in a whisker-reinforced metal. Mater Sci Eng 125: 203–213. doi: 10.1016/0921-5093(90)90170-8
[16]	Gambarotta L (2004) Friction-damage coupled model for brittle materials. Eng Fract Mech 71: 829–836. doi: 10.1016/S0013-7944(03)00020-1
[17]	Gambarotta L, Logomarsino S (1997) Damage models for the seismic response of brick masonry shear walls. Part I: the mortar joint model and its application. Earthq Eng Struct D 26: 423–439.
[18]	Alfano G, Sacco E (2006) Combining interface damage and friction in a cohesive-zone model. Int J Numer Meth Eng 68: 542–582. doi: 10.1002/nme.1728
[19]	Parrinello F, Failla B, Borino G (2009) Cohesive-frictional interface constitutive model. Int J Solids Struct 46: 2680–2692. doi: 10.1016/j.ijsolstr.2009.02.016
[20]	Parrinello F, Marannano G, Borino G, et al. (2013) Frictional effect in mode II delamination: Experimental test and numerical simulation. Eng Fract Mech 110: 258–269. doi: 10.1016/j.engfracmech.2013.08.005
[21]	Parrinello F, Marannano G, Borino G (2016) A thermodynamically consistent cohesive-frictional interface model for mixed mode delamination. Eng Fract Mech 153: 61–79. doi: 10.1016/j.engfracmech.2015.12.001
[22]	Simone A (2004) Partition of unity-based discontinuous elements for interface phenomena: computational issues. Int J Numer Meth Bio 20: 465–478.
[23]	Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Meth Eng 45: 601–620. doi: 10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S
[24]	Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Meth Eng 46: 131–150. doi: 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J
[25]	Sukumar N, Moës N, Moran N, et al. (2000) Extended finite element method for threedimensional crack modelling. Int J Numer Meth Eng 48: 1549–1570. doi: 10.1002/1097-0207(20000820)48:11<1549::AID-NME955>3.0.CO;2-A
[26]	Belytschko T, Moës N, Usui S, et al. (2001) Arbitrary discontinuities in finite elements. Int J Numer Meth Eng 50: 993–1013. doi: 10.1002/1097-0207(20010210)50:4<993::AID-NME164>3.0.CO;2-M
[27]	Sukumar N, Chopp DL, Moës N, et al. (2000) Modelling holes and inclusions by level sets in the extended finite element method. Comput Method Appl M 190: 6183–6200.
[28]	Belytschko T, Moës N (2002) Extended finite element method for cohesive crack growth. Eng Fract Mech 69: 813–883. doi: 10.1016/S0013-7944(01)00128-X
[29]	Wells GN, Sluys LJ (2001) A new method for modelling cohesive cracks using finite elements. Int J Numer Meth Eng 50: 2667–2682. doi: 10.1002/nme.143
[30]	Zi G, Belytschko T (2003) New crack-tip elements for XFEM and applications to cohesive cracks. Int J Numer Meth Eng 57: 2221–2240. doi: 10.1002/nme.849
[31]	Hettich T, Ramm E (2006) Interface material failure modeled by the extended finite-element method and level sets. Comput Method Appl M 195: 4753–4767. doi: 10.1016/j.cma.2005.09.022
[32]	Khoei AR, Nikbakht M (2007) An enriched finite element algorithm for numerical computation of contact friction problems. Int J Mech Sci 49: 183–199. doi: 10.1016/j.ijmecsci.2006.08.014
[33]	Moës N, Cloirec M, Cartraud P, et al. (2003) A computational approach to handle complex microstructure geometries. Comput Method Appl M 192: 3163–3177. doi: 10.1016/S0045-7825(03)00346-3
[34]	Drau K, Chevaugeon N, Moës N (2010) Studied X-FEM enrichment to handle material interfaces with higher order finite element. Comput Method Appl M 199: 1922–1936. doi: 10.1016/j.cma.2010.01.021
[35]	Lemaitre J, Chaboche JL (1990) Mechanics of solids materials, Cambridge University Press.
[36]	Coleman BD, Noll W (1963) The thermodynamics of elastic materials with heat conduction and viscosity. Arch Ration Mech An 13: 167–178. doi: 10.1007/BF01262690
[37]	Coleman B (1971) Thermodynamics of Materials with Memory, CISM, Springer.
[38]	Zienkiewicz OC, Taylor RL (2000) The finite element method: solid mechanics, Butterworth-Heinemann.
[39]	Paggi M, Wriggers P (2016) Node-to-segment and node-to-surface interface finite elements for fracture mechanics. Comput Method Appl M 300: 540–560. doi: 10.1016/j.cma.2015.11.023
[40]	Nguyen VP, Nguyen CT, Bordas S, et al. (2016) Modelling interfacial cracking with non-matching cohesive interface elements. Comput Mech 58: 731–746. doi: 10.1007/s00466-016-1314-y

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