Homogenization of composites with interfacial debonding using duality-based solver and micromechanics

• Autorzy: Gruber P. , Zeman J. , Kruis J. , Šejnoha M.
• Języki publikacji: EN

Abstrakty

EN

One of the key aspects governing the mechanical performance of composite materials is debonding: the local separation of reinforcing constituents from matrix when the interfacial strength is exceeded. In this contribution, two strategies to estimate the overall response of particulate composites with rigidbrittle interfaces are investigated, The first approach is based on a detailed numerical representation of a composite microstructure. The resulting problem is discretized using the Finite Element Tearing and Interconnecting method, which, apart from computational efficiency, allows for an accurate representation of interfacial tractions as well as mutual inter-phase contact conditions. The candidate solver employs the assumption of uniform fields within the composite estimated using the Mori-Tanaka method. A set of representative numerical examples is presented to assess the added value of the detailed numerical model over the simplified micromechanics approach.

Słowa kluczowe

EN

first-order homogenization; particulate composites; debonding; FETI method; micromechanics

PL

homogenizacja pierwszego rzędu; kompozyt; mikromechanika

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2009
• Tom: Vol. 16, No. 1
• Strony: 59--76
• Opis fizyczny: Bibliogr. 48 poz., il., wykr.

Twórcy

autor

Gruber P.

autor

Zeman J.

autor

Kruis J.

autor

Šejnoha M.

• Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, 166 29 Prague 6, Czech Republic

Bibliografia

• [1] J. Alberty, C. Carstensen, S.A. Funken, R. Klose. MATLAB implementation of the finite element method in elasticity. Computing, 69(3): 239-263, 2002.
• [2] P.M.A. Areias, T. Rabczuk. Quasi-static crack propagation in piane and piate structures using set-valued traction-separation laws. International Journal for Numerical Methods in engineering, 74(3): 475-505, 2008.
• [3] Y. Benyeniste. The effective mechanical behaviour of composite materials with imperfect contact between the constituents. Mechanics of Materials, 4(2): 197-208, 1985.
• [4] Y. Benyeniste. A new approach to the application of Mori-Tanaka theory in composite materials. Mechanics of Materials, 6(2): 147-157, 1987.
• [5] Z. Bittnar, J. Sejnoha. Numerical methods in structural mechanics. ASCE Press and Thomas Telford, Ltd, New York and London, 1996. [6] M.K. Chati, A.K. Mitra. Prediction of elastic properties of fiber-reinforced unidirectional composites. Engineering Analysis With Boundary Elements, 21(3): 235-244, 1999
• [7] B. Cox, Q. Yang. In ąuest of virtual tests for structural composites. Science, 314(5802): 1102-1107, 2006.
• [8] C. Dóbert, R. Mahnken, E. Stein. Numerical simulation of interface debonding with a combined damage friction constitutive model. Computational Mechanics, 25(5): 456-467, 2000.
• [9] Z. Dong, A. J. Levy. Mean field estimates of the response of fiber composites with nonlinear interface. Mechanics of Materials, 32(12): 739-767, 2000.
• [10] Z. Dostal. Optimal quadratic programming algorithms with applications to variational inegualities. Vol. 23 of Springer Optimization and Its Applications. Springer Verlag, New York, NY, USA, 2009.
• [11] Z. Dostal, D. Horak, O. Vlach. FETI-based algorithms for modelling of fibrous composite materials with debonding. Mathematics and Computers in Simulation, 76(1-3): 57-64, 2007.
• [12] C. Farhat, J. Mandel, F.-X. Roux. Optimal convergence properties of the FETI domain decomposition method. Computer Methods in Applied Mechanics and Engineering, 115: 365-385, 1994.
• [13] C. Farhat, F.-X. Roux. A method of finite element tearing and interconnecting and its parallel solution algorithm. International Journal for Numerical Methods in Engineering, 32(6): 1205-1227, 1991.
• [14] F. Feyel, J.-L. Chaboche. FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials. Computer Methods in Applied Mechanics and Engineering, 183(3-4): 309-330, 2000.
• [15] M. Gosz, B. Moran, J.D. Achenbach. On the role of interphases in the transverse failure of fiber composites. International Journal of Damage Mechanics, 3(4): 357-377, 1994.
• [16] P. Gruber. FETI-based homogenization of composites with perfect bonding and debonding of constituents. Bulletin of Applied Mechanics, 4(13): 11-17, 2008. http://bulletin-am.cz/index.php/vam/article/view/84.
• [17] P. Gruber. Homogenization of Composite Materials with Imperfect Bonding of Constituents. Master's thesis, Czech Technical University in Prague, 2008. (in Czech) http://mech.fsv.cvut.cz/ grubepav/download/gruber_aster_thesis.pdf, [January 27, 2009].
• [18] Z. Hashin. Thermoelastic properties of fiber composites with imperfect interface. Mechanics of Materials, 8(4): 333-348, 1990.
• [19] H. M. Inglis, P. H. Geubelle, K. Matous, H. Tan, Y. Huang. Cohesive modeling of dewetting in particulate composites: Micromechanics vs. multiscale finite element analysis. Mechanics of Materials, 39(6): 580-595, 2007.
• [20] T. Kanit, S. Forest, I. Galliet, V. Mounoury, D. Jeulin. Determination of the size of the representative volume element for random composites: statistical and numerical approach. International Journal of Solids and Structures, 40(13-14): 3647-3679, 2003.
• [21] V. Kouznetsova, W. A. M. Brekelmans, P. T. Baaijens. An approach to micro-macro modeling of heterogeneous materials. Computational Mechanics, 27(1): 37-48, 2001.
• [22] J. Kruis. Domain Decomposition Methods for Distributed Computing. Saxe-Coburg Publications, Kippen, Stirling, Scotland, 2006.
• [23] J. Kruis, Z. Bittnar. Reinforcement-matrix interaction modeled by FETI method. In: U. Langer, M. Discacciati, D. E. Keyes, O. B. Widlund, W. Zulehner, eds., Domain Decomposition Methods in Science and Engineering XVII. Vol. 60 of Lecture Notes in Computational Science and Engineering, 567-573. Springer Yerlag, 2008.
• [24] S. Li, S. Ghosh. Debonding in composite microstructures with morphological variations. International Journal of Computational Methods, 1(1): 121-149, 2004.
• [25] K. Matous, H.M. Inglis, X. Gu, D. Rypl, T.L. Jackson, P.H. Geubelle. Multiscale modeling of solid propellants: from particle packing to failure. Composites Science and Technology, 67(7-8): 1694-1708, 2007.
• [26] J.C. Michel, H. Moulinec, P. Suąuet. Effective properties of composite materials with periodic microstructure: A Computational approach. Computer Methods in Applied Mechanics and Engineering, 172(1-4): 109-143, 1999.
• [27] G.W. Milton. The Theory of Composites. Vol. 6 of Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, 2002.
• [28] T. Mori, K. Tanaka. Average stress in matrix and average elastic energy of elastic materials with misfitting inclusions. Acta Metallurgica, 21(5): 571-573, 1973.
• [29] N.J. Pagano, G.P. Tandon. Modeling of imperfect bonding in fiber reinforced brittle matrix composites. Mechanics of Materials, 9(1): 49-64, 1990.
• [30] S.S. Pendhari, T. Kant, Y.M. Desai. Application of polymer composites in civil construction: A general review. Composite Structures, 84(2): 114-124, 2008.
• [31] P.-O. Persson, G. Strang. A simple mesh generator in MATLAB. SIAM Reuiew, 46(2): 329-345, 2004.
• [32| P. Ponte Castaneda, J.R. Willis. The effect of spatial distribution on the effective behaviour of composite materials and cracked media. Journal of the Mechanics and Physics of Solids, 43(12): 1919-1951, 1995.
• [33] P. Prochazka. Homogenization of linear and of debonding composites using the BEM. Engineering Analysis with Boundary Elements, 25(9): 753-769, 2001.
• [34] P. Prochazka, M. Śejnoha. Development of debond region oflag model. Computers & Structures, 55(2): 249-260, 1995.
• [35] A. Rekik, F. Auslender, M. Bornert, A. Zaoui. Objective evaluation of linearization procedures in nonlinear homogenization: A methodology and some implications on the accuracy of micromechanical schemes. International Journal of Solids and Structures, 44(10): 3468-3496, 2007.
• [36] K. Rektorys. Variational Methods in Mathematics, Science and Engineering. Springer Verlag, second edn., 2007.
• [37] J.C.J. Schellekens, R. De Borst. On the numerical integration of interface elements. International Journal for Numerical Methods in Engineering, 36(1): 43-66, 1993.
• [38] H. Tan, Y. Huang, C. Liu, P.H. Geubelle. The Mori-Tanaka method for composite materials with nonlinear interface debonding. International Journal of Plasticity, 21(10): 1890-1918, 20C5.
• [39] G. P. Tandon, N. J. Pagano. Effective thermoelastic moduli of a unidirectional fiber composite containing interfacial arc microcracks. Journal of Applied Mechanics, 63(1): 210-217, 1996.
• [40] H. Teng. Transverse stiffness properties of unidirectional fiber composites containing debonded fibers. Composites Part A: Applied Science and Manufacturing, 38(3): 682-690, 2007.
• [41] O. Vlach. Modelling of composites using duality-based solvers. Master's thesis, Technical University of Ostrava, 2001. (in Czech)
• http://dspace.vsb.cz/handle/10084/41719, [January 27, 2009].
• [42] M. Sejnoha, M. Srinivas. Modeling of effective properties of composites with intarfacial microcracks using PHA model. Building Research Journal, 46(2): 99-108, 1998.
• [43] M. Sejnoha, R. Yalenta, J. Zeman. Nonlinear viscoelastic analysis of statistically homogeneous random composites. International Journal for Multiscale Computational Engineering, 2(4): 644-672, 2004.
• [44] L.J. Walpole. On the overall elastic module of composite materials. Journal of the Mechanics and Physics of Solids, 17(4): 235-251, 1969.
• [45] M. E. Walter, G. Ravichandran, M. Ortiz. Computational modeling of damage evolution in unidirectional fiber reinforced ceramic matrix composites. Computational Mechanics, 20(1): 192-198, 1997.
• [46] P. Wriggers, G. Zavarise, T.I. Zohdi. A computational study of interfacial debonding damage in fibrous composite materials. Computational Materials Science, 12(1): 39-56, 1998.
• [47] J. Zeman, M. Sejnoha. Numerical evaluation of effective elastic properties of graphite fiber tow impregnated by polymer matrix. Journal of the Mechanics and Physics of Solids, 49(1): 69-90, 2001.
• [48] J. Zeman, M. Sejnoha. Prom random microstructures to representative volume elements. Modelling and Simulation in Materials Science and Engineering, 15(4): S325-S335, 2007.