Modeling elastic properties of composites using asymptotic averaging method with imperfect interface

A. P. Sokolov ; V. N. Shchetinin ; M. Yu. Kozlov

Matematičeskoe modelirovanie, Tome 32 (2020) no. 8, pp. 119-138.

Résumé

The paper presents a modification of the asymptotic averaging method for solving the elastic properties homogenization problem for composite materials, taking into account the phases interface elasticity. The conditions of a soft imperfect interface are considered, which allow a displacements jump on phases boundary. A literature review of methods for the interface modeling in composite materials is presented. The finite element method is used for the numerical implementation of an averaging method. A model of a surface interface finite element is proposed. The numerical method of elastic properties averaging is adapted to the presence of a discontinuity in the displacement field. Application boundaries of the soft imperfect interface are estimated in terms of interphase layer properties ranges. The problem of interface parameters identification by experimental data is considered. Computational experiments are conducted for dispersed-reinforced and unidirectional composite with isotropic inclusion.

Détail

Keywords: composite materials, homogenization, asymptotic averaging method, effective properties of composites, imperfect interface, soft imperfect interface, finite element method, interface finite element, interphase layer, adhesion, parametric identification.

Bibliographie

[1] J. D. Achenbach, H. Zhu, “Effect of interfacial zone on mechanical behavior and failure of fiber-reinforced composites”, J. of the Mech. and Phys. of Sol., 37:3 (1989), 81–393 | DOI | MR

[2] V. E. Zgaevskij, IU. G. IAnovskij, “Mekhanicheskie kharakteristiki sloia makromolekul vblizi poverkhnosti napolnitelia”, Mekh. kompozits. mater. i konstruk., 3:1 (1997), 105–112

[3] P. G. Khalatur, “Computer simulation of thin polymer layers”, Makromol. Chem., Macromol. Symp., 44:1 (1991), 23–32 | DOI

[4] N. K. Balabaev, A. N. Vlasov, V. E. Zgaevskij, IU. N. Karnet, IU. G. IAnovskij, “Struktura i mikromekhanicheskie svojstva mezhfaznykh sloev polimernykh matrichnykh kompozitov”, Mekhanika kompozitsionnykh materialov i konstruktsij, 5:2 (1999), 109–123

[5] R. M. Christensen, K. H. Lo, “Solutions for effective shear properties in three phase sphere and cylinder models”, J. of the Mechanics and Physics of Solids, 27:4 (1979), 315–330 | DOI | Zbl

[6] Yozo Mikata, Minoru Taya, “Stress field in a coated continuous fiber composite subjected to thermomechanical loadings”, J. Compos. Mater., 19:6, November (1985), 554–578 | DOI

[7] Y. Benveniste, G. J. Dvorak, T. Chen, “Stress fields in composites with coated inclusions”, Mechanics of Materials, 7:4 (1989), 305–317 | DOI

[8] N. J. Pagano, G. P. Tandon, “Elastic response of multi-directional coated-fiber composites”, Composites Science and Technology, 31:4 (1988), 273–293 | DOI

[9] I. Sevostianov, R. Rodriguez-Ramos, R. Guinovart-Diaz, J. Bravo-Castillero, F. J. Sabina, “Connections between different models describing imperfect interfaces in periodic fiber-reinforced composites”, Intern. J. of Solids and Structures, 49:13 (2012), 1518–1525 | DOI

[10] M. Goland, E. Reissner, “The stresses in cemented joints”, J. Appl. Mech., 66 (1944), A17–A27

[11] Y. Benveniste, “The effective mechanical behaviour of composite materials with imperfect contact between the constituents”, Mechanics of Materials, 4:2 (1985), 197–208 | DOI

[12] Z. Hashin, “Thermoelastic properties of fiber composites with imperfect interface”, Mechanics of Materials, 8:4 (1990), 333–348 | DOI | MR

[13] Z. Hashin, “The spherical inclusion with imperfect interface”, J. of Applied Mechanics, 58:2 (1991), 444–449 | DOI

[14] Z. Hashin, “Thermoelastic properties of particulate composites with imperfect interface”, Journal of the Mechanics and Physics of Solids, 39:6 (1991), 745–762 | DOI | MR

[15] Z. Hashin, “Extremum principles for elastic heterogeneous media with imperfect interfaces and their application to bounding of effective moduli”, J. of the Mechanics and Physics of Solids, 40:4 (1992), 767–781 | DOI | MR | Zbl

[16] Z. Hashin, “Thin interphase/imperfect interface in elasticity with application to coated fiber composites”, J. of the Mechanics and Physics of Solids, 50:12 (2002), 2509–2537 | DOI | MR | Zbl

[17] P. Bövik, “On the modelling of thin interface layers in elastic and acoustic scattering problems”, Quarterly J. of Mechanics and Appl. Math., 47:1, February (1994), 17–42 | DOI | MR | Zbl

[18] Y. Benveniste, T. Miloh, “Imperfect soft and stiff interfaces in two-dimensional elasticity”, Mechanics of Materials, 33:6 (2001), 309–323 | DOI

[19] D. Caillerie, J. C. Nedelec, “The effect of a thin inclusion of high rigidity in an elastic body”, Mathematical Methods in the Applied Sciences, 2:3 (1980), 251–270 | DOI | MR | Zbl

[20] Y. Benveniste, “A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media”, J. of the Mechanics and Physics of Solids, 54:4 (2006), 708–734 | DOI | MR | Zbl

[21] A. Klarbring, “Derivation of a model of adhesively bonded joints by the asymptotic expansion method”, Intern. J. of Engineering Science, 29:4 (1991), 493–512 | DOI | MR | Zbl

[22] A. Klarbring. A.B. Movchan, “Asymptotic modelling of adhesive joints”, Mechanics of Materials, 28:1–4 (1998), 137–145 | DOI

[23] G. Geymonat, F. Krasucki, S. Lenci, “Mathematical analysis of a bonded joint with a soft thin adhesive”, Mathematics and Mechanics of Solids, 4:2 (1999), 201–225 | DOI | MR

[24] F. Lebon, R. Rizzoni, S. Ronel, C. Licht, “Analysis of non-linear soft thin interfaces”, The Sixth Intern. Conf. on Comp. Structures Technology (September, 2002), 155–156

[25] F. Lebon, S. Ronel, “Asymptotic analysis of Mohr–Coulomb and Drucker–Prager soft thin layers”, Steel and Composite Structures, Techno-press, 4 (2004), 133–147 | DOI

[26] F. Lebon, R. Rizzoni, “Asymptotic behavior of a hard thin linear elastic interphase: an energy approach”, Intern. J. of Solids and Structures, 48:3–4 (2011), 441–449 | DOI | MR | Zbl

[27] R. Rizzoni, S. Dumont, F. Lebon, E. Sacco, “Higher order model for soft and hard elastic interfaces”, Intern. J. of Solids and Structures, 51:23–24 (2014), 4137–4148 | DOI

[28] N. S. Bakhvalov, G. P. Panasenko, Homogenization: averaging processes in periodic media. Mathematical problems in mechanics of composite materials, Mathematics and its applications, 36, Kluwer academic publishers, Dordrecht–Boston–London, 1989, 34 pp. | DOI | MR

[29] B. E. Pobedria, Mechanics of composite materials, MGU, M., 1984

[30] K. A. Wilkinson, D. A. Ordonez, Adhesive properties in nanomaterials, Nova Science Publishers, Inc, 2011, 188 pp.

[31] F. Lebon, S. Dumont, R. Rizzoni, J. C. López-Realpozo, R. Guinovart-Díaz, R. Rodríguez-Ramos, J. Bravo-Castillero, F. J. Sabina, “Soft and hard anisotropic interface in composite materials”, Composites Part B: Engineering, Elsevier, 90 (2016), 58–68 | DOI

[32] R. Rodríguez-Ramos, R. de Medeiros, R. Guinovart-Díaz, J. Bravo-Castillero, J. A. Otero, V. Tita, “Different approaches for calculating the effective elastic properties in composite materials under imperfect contact adherence”, Composite Struct., Elsevier, 99 (2013), 264–275 | DOI

[33] Y. I. Dimitrienko, A. P. Sokolov, “Elastic properties of composite materials”, Mathematical Models and Computer Simulations, 2:1 (2010), 116–130 | DOI

[34] IU. I. Dimitrienko, A. P. Sokolov, “CHislennoe modelirovanie kompozitsionnykh materialov s mnogourovnevoj strukturoj”, Izv. RAN. Fizicheskaia ser., 75:11 (2011), 1551–1556

[35] P. Rahul-Kumar, A. Jagota, S. J. Bennison, S. Saigal, S. Muralidhar, “Polymer interfacial fractu?re simulations using cohesive elements”, Acta Materialia, 47:15–16 (1999), 4161–4169 | DOI

[36] W. G. Jiang, R. Z. Zhong, Q. H. Qin, Y. G. Tong, “Homogenized finite element analysis $n$ effective elastoplastic mechanical behaviors of composite with imperfect interfaces”, Intern. Journal of Molecular Sciences, 15:12 (2014), 23389–23407 | DOI

[37] S. Guessasma, N. Benseddiq, D. Lourdin, “Effective Young?s modulus of biopolymer composites with imperfect interface”, Int. J. of Solids and Struct., Elsev., 47:18–19 (2010), 2436–2444 | DOI | Zbl

[38] A. A. Nasedkina, A. Rajagopal, “Mathematical and computer homogenization models for bulk mixture composite materials with imperfect interfaces”, Materials Physics and Mechanics, 37:1 (2018), 31–34

[39] M. Hamsasew, W. S. Yu., “A micromechanical approach to imperfect interface analysis of heterogeneous materials”, 56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (2015)

[40] V. Schetinin, Kh. Dmitriy, nla3d open source FEM framework, , 2018 https://github.com/dmitryikh/nla3d/

[41] A. P. Sokolov, V. N. Shchetinin, “Identifikatsiia uprugikh svojstv adgezionnogo sloia dispersno-armirovannykh kompozitnykh materialov na osnove eksperimentalnykh dannykh”, Mekhanika kompozitsionnykh materialov i konstruktsij, 24:4 (2018), 555–581 | DOI

[42] O. C. Zienkiewicz, The finite element method in engineering science, McGraw-Hill, London–New York, 1971, 521 pp. | MR | Zbl

[43] J. Smith, “Experimental values for the elastic constants of a particulate filled glassy polymer”, J. Res. NBS., 80A:1 (1976), 45–49 | DOI

[44] P. D. Soden, M. J. Hinton, A. S. Kaddour, “Lamina properties, lay-up configurations and loading conditions for a range of fibre-reinforced composite laminates”, Composites Science and Technology, 58:7 (1998), 1011–1022 | DOI