Coherent energetic interfaces accounting for in-plane degradation
Source abstract
Abstract
Interfaces can play a dominant role in the overall response of a body. The importance of interfaces is particularly appreciated at small length scales due to large area to volume ratios. From the mechanical point of view, this scale dependent characteristic can be captured by endowing a coherent interface with its own elastic resistance as proposed by the interface elasticity theory. This theory proves to be an extremely powerful tool to explain size effects and to predict the behavior of nano-materials. To date, interface elasticity theory only accounts for the elastic response of coherent interfaces and obviously lacks an explanation for inelastic interface behavior such as damage or plasticity. The objective of this contribution is to extend interface elasticity theory to account for damage of coherent interfaces. To this end, a thermodynamically consistent interface elasticity theory with damage is proposed. A local damage model for the interface is presented and is extended towards a non-local damage model. The non-linear governing equations and the weak forms thereof are derived. The numerical implementation is carried out using the finite element method and consistent tangents are listed. The computational algorithms are given in detail. Finally, a series of numerical examples is studied to provide further insight into the problem and to carefully elucidate key features of the proposed theory.
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Research context
OpenAlex topics: Numerical methods in engineering · Composite Material Mechanics · Fatigue and fracture mechanics
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References (100+)
Show source-provided references
1. Alfano G, Crisfield MA (2001) Finite element interface models for the delamination analysis of laminated composites: Mechanical and computational issues. Int J Numer Methods Eng 50:1701–173610.1002/nme.93 ↗
2. Alfano G, Sacco E (2006) Combining interface damage and friction in a cohesive-zone model. Int J Numer Methods Eng 68(5):542–58210.1002/nme.1728 ↗
3. Allix O, Ladevéze P, Corigliano A (1995) Damage analysis of interlaminar fracture specimens. Compos Struct 31(1):61–7410.1016/0263-8223(95)00002-X ↗
4. Allix O, Corigliano A (1996) Modeling and simulation of crack propagation in mixed-modes interlaminar fracture specimens. lnt J Fract 77(2):111–14010.1007/BF00037233 ↗
5. Andrade FXC, Sá JMACD, Pires FMA (2011) A ductile damage nonlocal model of integral-type at finite strains: formulation and numerical issues. Int J Damage Mech 20(4):515–55710.1177/1056789510386850 ↗
6. Andrade F, Sá JCD, Pires FA (2014) Assessment and comparison of non-local integral models for ductile damage. Int J Damage Mech 23(2):261–29610.1177/1056789513493103 ↗
7. Aragón AM, Soghrati S, Geubelle PH (2013) Effect of in-plane deformation on the cohesive failure of heterogeneous adhesives. J Mech Phys Solids 61(7):1600–161110.1016/j.jmps.2013.03.003 ↗
8. Askes H, Sluys LJ (2000) Remeshing strategies for adaptive ALE analysis of strain localisation. Eur J Mech A Solids 19(3):447–46710.1016/S0997-7538(00)00176-5 ↗
9. Barenblatt GI (1962) The mathematical theory of equilibrium cracks in brittle fracture. Advances in applied mechanics 7(1):55–12910.1016/S0065-2156(08)70121-2 ↗
10. Bažant ZP (1994) Nonlocal damage theory based on micromechanics of crack interactions. J Eng Mech 120(3):593–61710.1061/(ASCE)0733-9399(1994)120:3(593) ↗
11. Bažant ZP, Cabot GP (1989) Measurement of characteristic length of nonlocal continuum. J Eng Mech 115(4):755–76710.1061/(ASCE)0733-9399(1989)115:4(755) ↗
12. Bažant ZP, Jirásek M (2002) Nonlocal integral formulations of plasticity and damage: survey of progress. J Eng Mech 128(11):1119–114910.1061/(ASCE)0733-9399(2002)128:11(1119) ↗
13. Bažant ZP, Xi Y (1991) Statistical size effect in quasibrittle structures: II. Nonlocal theory. J Eng Mech 117(11):2623–264010.1061/(ASCE)0733-9399(1991)117:11(2623) ↗
14. Benveniste Y (2006) A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media. J Mech Phys Solids 54(4):708–73410.1016/j.jmps.2005.10.009 ↗
15. Benveniste Y (2013) Models of thin interphases and the effective medium approximation in composite media with curvilinearly anisotropic coated inclusions. Int J Eng Sci 72:140–15410.1016/j.ijengsci.2013.07.003 ↗
16. Benveniste Y, Miloh T (2001) Imperfect soft and stiff interfaces in two-dimensional elasticity. Mech Mater 33(6):309–32310.1016/S0167-6636(01)00055-2 ↗
17. Bolzon G, Corigliano A (1997) A discrete formulation for elastic solids with damaging interfaces. Comput Methods Appl Mech Eng 140(3–4):329–35910.1016/S0045-7825(96)01101-2 ↗
18. Cabot GP, Bažant ZP (1987) Nonlocal damage theory. J Eng Mech 113(10):1512–153310.1061/(ASCE)0733-9399(1987)113:10(1512) ↗
19. Cammarata RC (1997) Surface and interface stress effects on interfacial and nanostructured materials. Mater Sci Eng A 237(2):180–18410.1016/S0921-5093(97)00128-7 ↗
20. Carmeliet J (1999) Optimal estimation of gradient damage parameters from localization phenomena in quasi-brittle materials. Mech Cohes Frict Mater 4(1):1–1610.1002/(SICI)1099-1484(199901)4:1<1::AID-CFM54>3.0.CO;2-F ↗
21. Cazes F, Coret M, Combescure A, Gravouil A (2009) A thermodynamic method for the construction of a cohesive law from a nonlocal damage model. Int J Solids Struct 46(6):1476–149010.1016/j.ijsolstr.2008.11.019 ↗
22. Chaboche JL (1981) Continuous damage mechanics—a tool to describe phenomena before crack initiation. Nucl Eng Des 64(2):233–24710.1016/0029-5493(81)90007-8 ↗
23. Chaboche JL (1984) Anisotropic creep damage in the framework of continuum damage mechanics. Nucl Eng Des 79(3):309–31910.1016/0029-5493(84)90046-3 ↗
24. Chaboche JL, Girard R, Schaff A (1997) Numerical analysis of composite systems by using interphase/interface models. Comput Mech 20:3–1110.1007/s004660050209 ↗
25. Chatzigeorgiou G, Javili A, Steinmann P (2013) Multiscale modelling for composites with energetic interfaces at the micro- or nanoscale. Math Mech Solids10.1177/1081286513516122 ↗
26. Chen J, Crisfield M, Kinloch AJ, Busso EP, Matthews FL, Qiu Y (1999) Predicting progressive delamination of composite material specimens via interface elements. Mech Compos Mater Struct 6(4):301–31710.1080/107594199305476 ↗
27. Cordero NM, Forest S, Busso EP (2015) Second strain gradient elasticity of nano-objects. J Mech Phys Solids. doi: 10.1016/j.jmps.2015.07.01210.1016/j.jmps.2015.07.012 ↗
28. Corigliano A (1993) Formulation, identification and use of interface models in the numerical analysis of composite delamination. Int J Solids Struct 30(20):2779–281110.1016/0020-7683(93)90154-Y ↗
29. Daher N, Maugin GA (1986) The method of virtual power in continuum mechanics application to media presenting singular surfaces and interfaces. Acta Mech 60(3–4):217–24010.1007/BF01176354 ↗
30. Davydov D, Javili A, Steinmann P (2013) On molecular statics and surface-enhanced continuum modeling of nano-structures. Comput Mater Sci 69:510–51910.1016/j.commatsci.2012.11.053 ↗
31. de Souza Neto EA, Perić D, Owen DRJ (1994a) A model for elastoplastic damage at finite strains: algorithmic issues and applications. Eng Comput 11(3):257–28110.1108/02644409410799272 ↗
32. de Souza Neto EA, Perić D, Owen DRJ (1994b) A phenomenological three-dimensional rate-idependent continuum damage model for highly filled polymers: formulation and computational aspects. J Mech Phys Solids 42(10):1533–155010.1016/0022-5096(94)90086-8 ↗
33. de Souza Neto EA, Perić D, Owen DRJ (1998) Continuum modelling and numerical simulation of material damage at finite strains. Arch Comput Methods Eng 5(4):311–38410.1007/BF02905910 ↗
34. de Souza Neto EA, Peric D, Owen DRJ (2011) Computational methods for plasticity: theory and applications. Wiley, London
35. de Souza Neto EA, Perić D (1996) A computational framework for a class of fully coupled models for elastoplastic damage at finite strains with reference to the linearization aspects. Comput Methods Appl Mech Eng 130(1–2):179–19310.1016/0045-7825(95)00872-1 ↗
36. dell’Isola F, Romano A (1987) On the derivation of thermomechanical balance equations for continuous systems with a nonmaterial interface. Int J Eng Sci 25:1459–146810.1016/0020-7225(87)90023-1 ↗
37. Dingreville R, Qu J, Cherkaoui M (2005) Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films. J Mech Phys Solids 53(8):1827–185410.1016/j.jmps.2005.02.012 ↗
38. Duan HL, Karihaloo BL (2007) Effective thermal conductivities of heterogeneous media containing multiple imperfectly bonded inclusions. Phys Rev B 75(6):064,206
39. Duan HL, Wang J, Huang ZP, Karihaloo BL (2005a) Eshelby formalism for nano-inhomogeneities. Proc R Soc A Math Phys Eng Sci 461(2062):3335–335310.1098/rspa.2005.1520 ↗
40. Duan HL, Wang J, Huang ZP, Karihaloo BL (2005b) Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress. J Mech Phys Solids 53(7):1574–159610.1016/j.jmps.2005.02.009 ↗
41. Duan HL, Wang J, Karihaloo BL (2009) Theory of elasticity at the nanoscale. Adv Appl Mech 42:1–6810.1016/S0065-2156(08)00001-X ↗
42. Eringen AC (1966) A unified theory of thermomechanical materials. Int J Eng Sci 4(2):179–20210.1016/0020-7225(66)90022-X ↗
43. Fagerström M, Larsson R (2008) A thermo-mechanical cohesive zone formulation for ductile fracture. J Mech Phys Solids 56(10):3037–305810.1016/j.jmps.2008.06.002 ↗
44. Fischer FD, Waitz T, Vollath D, Simha NK (2008) On the role of surface energy and surface stress in phase-transforming nanoparticles. Prog Mater Sci 53(3):481–52710.1016/j.pmatsci.2007.09.001 ↗
45. Fischer FD, Svoboda J (2010) Stresses in hollow nanoparticles. Int J Solids Struct 47(20):2799–280510.1016/j.ijsolstr.2010.06.008 ↗
46. Fleischhauer R, Behnke R, Kaliske M (2013) A thermomechanical interface element formulation for finite deformations. Comput Mech 52(5):1039–105810.1007/s00466-013-0862-7 ↗
47. Fried E, Todres R (2005) Mind the gap: the shape of the free surface of a rubber-like material in proximity to a rigid contactor. J Elast 80(1–3):97–15110.1007/s10659-005-9019-z ↗
48. Gurtin ME, Weissmüller J, Larché F (1998) A general theory of curved deformable interfaces in solids at equilibrium. Philos Mag A 78(5):1093–110910.1080/01418619808239977 ↗
49. Gurtin ME, Murdoch AI (1975) A continuum theory of elastic material surfaces. Arch Ration Mech Anal 57(4):291–32310.1007/BF00261375 ↗
50. Haiss W (2001) Surface stress of clean and adsorbate-covered solids. Rep Prog Phys 64(5):59110.1088/0034-4885/64/5/201 ↗
51. Holzapfel GA (2000) Nonlinear Solid mechanics: a continuum approach for engineering. Wiley, London
52. Huang ZP, Sun L (2007) Size-dependent effective properties of a heterogeneous material with interface energy effect: From finite deformation theory to infinitesimal strain analysis. Acta Mech 190(1–4):151–16310.1007/s00707-006-0381-0 ↗
53. Ijaz H, Asad M, Gornet L, Alam SY (2014) Prediction of delamination crack growth in carbon/fiber epoxy composite laminates using non-local interface damage model. Mech Ind 15(4):293–30010.1051/meca/2014030 ↗
54. Javili A, McBride A, Steinmann P (2012) Numerical modelling of thermomechanical solids with mechanically energetic (generalised) Kapitza interfaces. Comput Mater Sci 65:542–55110.1016/j.commatsci.2012.06.006 ↗
55. Javili A, dell’Isola F, Steinmann P (2013a) Geometrically nonlinear higher-gradient elasticity with energetic boundaries. J Mech Phys Solids 61(12):2381–240110.1016/j.jmps.2013.06.005 ↗
56. Javili A, McBride A, Steinmann P (2013b) Numerical modelling of thermomechanical solids with highly conductive energetic interfaces. Int J Numer Meth Eng 93(5):551–57410.1002/nme.4402 ↗
57. Javili A, McBride A, Steinmann P (2013c) Thermomechanics of solids with lower-dimensional energetics: on the importance of surface, interface, and curve structures at the nanoscale. A unifying review. Appl Mech Rev 65(1):01080210.1115/1.4023012 ↗
58. Javili A, Kaessmair S, Steinmann P (2014a) General imperfect interfaces. Comput Methods Appl Mech Eng 275:76–9710.1016/j.cma.2014.02.022 ↗
59. Javili A, McBride A, Steinmann P, Reddy BD (2014b) A unified computational framework for bulk and surface elasticity theory: a curvilinear-coordinate-based finite element methodology. Comput Mech 54(3):745–76210.1007/s00466-014-1030-4 ↗
60. Javili A, Steinmann P (2009) A finite element framework for continua with boundary energies. Part I: the two-dimensional case. Comput Methods Appl Mech Eng 198(27–29):2198–220810.1016/j.cma.2009.02.008 ↗
61. Javili A, Steinmann P (2010a) A finite element framework for continua with boundary energies. Part II: the three-dimensional case. Comput Methods Appl Mech Eng 199(9–12):755–76510.1016/j.cma.2009.11.003 ↗
62. Javili A, Steinmann P (2010b) On thermomechanical solids with boundary structures. Int J Solids Struct 47(24):3245–325310.1016/j.ijsolstr.2010.08.009 ↗
63. Jirasek M (1998) Nonlocal models for damage and fracture: comparison of approaches. Int J Solids Struct 35(31):4133–414510.1016/S0020-7683(97)00306-5 ↗
64. Jirásek M, Patzák B (2002) Consistent tangent stiffness for nonlocal damage models. Comput Struct 80(14–15):1279–129310.1016/S0045-7949(02)00078-0 ↗
65. Kachanov LM (1958) Time of the rupture process under creep conditions. Izv Akad Nauk SSR Otd Tech Nauk 8:26–31
66. Krajcinovic D, Fonseka GU (1981) Continuous damage theory of brittle materials—1. General theory. J Appl Mech Trans ASME 48(4):809–81510.1115/1.3157739 ↗
67. Krayani A, Pijaudier-Cabot G, Dufour F (2009) Boundary effect on weight function in nonlocal damage model. Eng Fract Mech 76(14):2217–223110.1016/j.engfracmech.2009.07.007 ↗
68. Ladevèze P, Allix O, Gornet L, Lévêque D, Perret L (1998) A computational damage mechanics approach for laminates: identification and comparison with experimental results. Stud Appl Mech 46:481–50010.1016/S0922-5382(98)80059-7 ↗
69. Lemaitre J (1984) Three-dimensional ductile damage model applied to deep-drawing forming limits. In: Proceedings of the $$4^{{\rm th}}$$ 4 th international conference on the mechanical behaviour of materials vol 2, pp 1047–105310.1016/B978-1-4832-8372-2.50132-9 ↗
70. Levitas VI, Javanbakht M (2010) Surface tension and energy in multivariant martensitic transformations: phase-field theory, simulations, and model of coherent interface. Phys Rev Lett 105(16):165–70110.1103/PhysRevLett.105.165701 ↗
71. Lin G, Geubelle PH, Sottos NR (2001) Simulation of fiber debonding with friction in a model composite pushout test. Int J Solids Struct 38(46–47):8547–856210.1016/S0020-7683(01)00085-3 ↗
72. Mazars J, Berthaud Y, Ramtani S (1990) The unilateral behaviour of damaged concrete. Eng Fract Mech 35(4):629–63510.1016/0013-7944(90)90145-7 ↗
73. McBride AT, Javili A, Steinmann P, Bargmann S (2011) Geometrically nonlinear continuum thermomechanics with surface energies coupled to diffusion. J Mech Phys Solids 59(10):2116–213310.1016/j.jmps.2011.06.002 ↗
74. Mi Y, Crisfield MA, Davies GAO, Hellweg HB (1998) Progressive delamination using interface elements. J Compos Mater 32(14):1246–127210.1177/002199839803201401 ↗
75. Moeckel GP (1975) Thermodynamics of an interface. Arch Ration Mech Anal 57(3):255–28010.1007/BF00280158 ↗
76. Mosler J, Scheider I (2011) A thermodynamically and variationally consistent class of damage-type cohesive models. J Mech Phys Solids 59(8):1647–166810.1016/j.jmps.2011.04.012 ↗
77. Murakami S, Ohno N (1981) A continuum theory of creep and creep damage. In: Ponter ARS, Hayhurst DR (eds) Creep in structures, international union of theoretical and applied mechanics. Springer, Berlin, pp 422–444
78. Murdoch AI (1976) A thermodynamical theory of elastic material interfaces. Q J Mech Appl Math 29(3):245–27510.1093/qjmam/29.3.245 ↗
79. Needleman A (1990) An analysis of tensile decohesion along an interface. J Mech Phys Solids 38(3):289–32410.1016/0022-5096(90)90001-K ↗
80. Needleman A (1992) Micromechanical modelling of interfacial decohesion. Ultramicroscopy 40:203–21410.1016/0304-3991(92)90117-3 ↗
81. Needleman A (2014) Some issues in cohesive surface modeling. Procedia IUTAM 10:221–24610.1016/j.piutam.2014.01.020 ↗
82. Özdemir I, Brekelmans WAM, Geers MGD (2010) A thermo-mechanical cohesive zone model. Comput Mech 46:735–74510.1007/s00466-010-0507-z ↗
83. Park HS, Klein PA (2007) Surface Cauchy–Born analysis of surface stress effects on metallic nanowires. Phys Rev B 75(085):408
84. Parrinello F, Failla B, Borino G (2009) Cohesive–frictional interface constitutive model. Int J Solids Struct 46(13):2680–269210.1016/j.ijsolstr.2009.02.016 ↗
85. Pijaudier-Cabot G, Dufour F (2010) Non local damage model: boundary and evolving boundary effects. Eur J Environ Civil Eng 14(6–7):729–74910.1080/19648189.2010.9693260 ↗
86. Pijaudier-Cabot G, Grégoire D (2014) A review of non local continuum damage: modelling of failure? Netw Heterog Media 9(4):575–59710.3934/nhm.2014.9.575 ↗
87. Pijaudier-Cabot G, Huerta A (1991) Finite element analysis of bifurcation in nonlocal strain softening solids. Comput Methods Appl Mech Eng 90(1–3):905–91910.1016/0045-7825(91)90190-H ↗
88. Rabotnov YN (1963) On the equation of state of creep. Proc Inst Mech Eng Conf Proc 178(1):2-117–2-122
89. Raous M (2011) Interface models coupling adhesion and friction. Comptes Rendus Mecanique 339(7–8):491–50110.1016/j.crme.2011.05.007 ↗
90. Saanouni K, Chaboche JL, Lesne PM (1989) On the creep crack-growth prediction by a non local damage formulation. Eur J Mech A Solids 8(6):437–459
91. Saouridis C, Mazars J (1992) Prediction of the failure and size effect in concrete via a bi-scale damage approach. Eng Comput 9(3):329–34410.1108/eb023870 ↗
92. Schellekens JCJ, Borst RD (1993) A non-linear finite element approach for the analysis of mode-I free edge delamination in composites. Int J Solids Struct 30(9):1239–125310.1016/0020-7683(93)90014-X ↗
93. Sharma P, Ganti S, Bhate N (2003) Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Appl Phys Lett 82(4):535–53710.1063/1.1539929 ↗
94. Sharma P, Ganti S (2004) Size-dependent Eshelbys tensor for embedded nano-inclusions incorporating surface/interface energies. J Appl Mech 71(5):663–67110.1115/1.1781177 ↗
95. Sharma P, Wheeler LT (2007) Size-dependent elastic state of ellipsoidal nano-inclusions incorporating surface/ interface tension. J Appl Mech 74(3):447–45410.1115/1.2338052 ↗
96. Simo JC, Hughes TJR (1998) Comput Inelast. Springer, New York
97. Simo JC, Ju JW (1987) Strain- and stress-based continuum damage models I: formulation. Int J Solids Struct 23(7):821–84010.1016/0020-7683(87)90083-7 ↗
98. Steigmann DJ, Ogden RW (1999) Elastic surface–substrate interactions. Proc R Soc Lond A Math Phys Eng Sci 455(1982):437–47410.1098/rspa.1999.0320 ↗
99. Steinmann P, Miehe C, Stein E (1994) Comparison of different finite deformation inelastic damage models within multiplicative elastoplasticity for ductile materials. Comput Mech 13(6):458–47410.1007/BF00374241 ↗
100. Steinmann P (1999) Formulation and computation of geometrically non-linear gradient damage. Int J Numer Meth Eng 46(5):757–77910.1002/(SICI)1097-0207(19991020)46:5<757::AID-NME731>3.0.CO;2-N ↗