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A multiscale strategy for thermo-elastic plastic stress analysis of heterogeneous multiphase materials. (English) Zbl 1329.74050

Summary: A multiscale strategy is developed for the thermo-elastic plastic stress analysis of heterogeneous multiphase materials. The strategy is based on the extended multiscale finite element method (EMsFEM) and the enriched partition of unity approach. In the formulation, the enriched numerical base functions are adapted into the EMsFEM, which show good applicability to the local deformation pattern. Thus, the microscopic variable fields can be reproduced precisely, which are crucial for the nonlinear analysis. Numerical examples of two-phase heterogeneous media with regular and irregular microstructures demonstrate the validity and efficiency of the proposed method.

MSC:

74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74F05 Thermal effects in solid mechanics
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[1] Nemat-Nasser S., Hori M.: Micromechanics: Overall Properties of Heterogeneous Materials. North-Holland, London (1993) · Zbl 0924.73006
[2] Hsu T.R.: The Finite Element Method in Thermomechanics, pp. 65-67. Allen & Unwin, Boston (1986)
[3] Wang M., Pan N.: Predictions of effective physical properties of complex multiphase materials. Mater. Sci. Eng. R 63, 1-30 (2008)
[4] Kanoute P., Boso D.P., Chaboche J.L., Schrefler B.A.: Multiscale methods for composites: a review. Arch. Comput. Methods Eng. 16, 31-75 (2009) · Zbl 1170.74304
[5] Weinan E., Engquist B., Li X., Ren W., Vanden-Eijnden E.: Heterogeneous multiscale methods: a review. Commun. Comput. Phys. 2, 367-450 (2007) · Zbl 1164.65496
[6] Eshelby J.D.: The determination of the field of an ellipsoidal inclusion and related problems. Proc. R. Soc. Lond. A 241, 376-396 (1957) · Zbl 0079.39606
[7] Hill R.: A self-consistent mechanics of composite materials. J. Mech. Phys. Solids 13, 213-222 (1965)
[8] Hashin Z., Shtrikman S.: A variational approach to the theory of the elastic behaviour of multiphase materials. J. Mech. Phys. Solids 11, 127-140 (1963) · Zbl 0108.36902
[9] Ibrahimbegovic A., Markovic D.: Strong coupling methods in multi-phase and multi-scale modeling of inelastic behavior of heterogeneous structures. Comput. Methods Appl. Mech. Eng. 192, 3089-3107 (2003) · Zbl 1054.74730
[10] Miehe C., Bayreuther C.G.: On multiscale FE analyses of heterogeneous structures: from homogenization to multigrid solvers. Int. J. Numer. Methods Eng. 71, 1135-1180 (2007) · Zbl 1194.74443
[11] Bensoussan A., Lions J.L., Papanicolau G.: Asymptotic Analysis for Periodic Structures. North-Holland, Amsterdam (1978) · Zbl 0404.35001
[12] Alzina A., Toussaint E., Béakou A.: Multiscale modeling of the thermoelastic behavior of braided fabric composites for cryogenic structures. Int. J. Solids Struct. 44, 6842-6859 (2007) · Zbl 1166.74328
[13] Zhang H.W., Zhang S., Bi J.Y., Schrefler B.A.: Thermo-mechanical analysis of periodic multiphase materials by a multiscale asymptotic homogenization approach. Int. J. Numer. Methods Eng. 69, 87-113 (2007) · Zbl 1129.74018
[14] Kouznetsova, V.: Computational homogenization for the multi-scale analysis of multi-phase materials. Ph.D. thesis, Eindhoven University of Technology, The Netherlands: Eindhoven (2002) · Zbl 0997.74069
[15] Özdemir I., Brekelmans W., Geers M.: \[{{\rm FE}^2}\] FE2 computational homogenization for the thermo-mechanical analysis of heterogeneous solids. Comput. Methods Appl. Mech. Eng. 198, 602-613 (2008) · Zbl 1228.74065
[16] Suquet P.M.: Local and global aspects in the mathematical theory of plasticity. In: Sawczuk, A., Bianchi, G. (eds) Plasticity Today: Modelling, Methods and Applications, pp. 279-310. Elsevier Applied Science Publishers, London (1985) · Zbl 1169.74597
[17] Terada, K., Kikuchi, N.: Nonlinear homogenization method for practical applications. In: Ghosh, S., Ostoja-Starzewski M. (eds.) Comput. Methods Micromech., ASME, AMD, vol. 212, pp. 1-16 (1995) · Zbl 1398.74429
[18] Smit R.J.M., Brekelmans W.A.M., Meijer H.E.H.: Prediction of the mechanical behaviour of non-linear heterogeneous systems by multi-level finite element modeling. Comput. Methods Appl. Mech. Eng. 155, 181-192 (1998) · Zbl 0967.74069
[19] Feyel F., Chaboche J.L.: \[{{\rm FE}^2}\] FE2 multiscale approach for modeling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials. Comput. Methods Appl. Mech. Eng. 183, 309-330 (2000) · Zbl 0993.74062
[20] Matsui K., Terada K., Yuge K.: Two-scale finite element analysis of heterogeneous solids with periodic microstructures. Comput. Struct. 82, 593-606 (2004)
[21] Lee K., Moorthy S., Ghosh S.: Multiple scale computational model for damage in composite materials. Comput. Methods Appl. Mech. Eng. 172, 175-201 (1999) · Zbl 0972.74063
[22] Fish J., Yu O., Shek K.: Computational damage mechanics for composite materials based on mathematical homogenization. Int. J. Numer. Methods Eng. 45, 1657-1679 (1999) · Zbl 0949.74057
[23] Jain J.R., Ghosh S.: Damage evolution in composites with a homogenization based continuum damage mechanics model. Int. J. Damage Mech. 18, 533-568 (2009)
[24] Markovic D., Niekamp R., Ibrahimbegovic A., Matthies H.G., Taylor R.L.: Multi-scale modeling of heterogeneous structures with inelastic constitutive behavior. Part I: Mathematical and physical aspects. Int. J. Eng. Comput. 22, 664-683 (2005) · Zbl 1186.74026
[25] Hautefeuille M., Colliat J.B., Ibrahimbegovic A., Matthies H., Villon P.: A multi-scale approach to model localized failure with softening. Comput. Struct. 94-95, 83-95 (2012)
[26] Zhang H.W., Wu J.K., Fu Z.D.: Extended multiscale finite element method for mechanical analysis of periodic lattice truss materials. Int. J. Multisc. Comput. 8, 597-613 (2010) · Zbl 1398.74429
[27] Zhang H.W., Wu J.K., Lü J., Fu Z.D.: Extended multiscale finite element method for mechanical analysis of heterogeneous materials. Acta Mech. Sin. 26, 899-920 (2010) · Zbl 1270.74196
[28] Babuška I., Osborn E.: Generalized finite element methods: their performance and their relation to mixed methods. SIAM J. Numer. Anal. 20, 510-536 (1983) · Zbl 0528.65046
[29] Babuška I., Caloz G., Osborn E.: Special finite element methods for a class of second order elliptic problems with rough coefficients. SIAM J. Numer. Anal. 31, 945-981 (1994) · Zbl 0807.65114
[30] Hou T.Y., Wu X.H.: A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys. 134, 169-189 (1997) · Zbl 0880.73065
[31] Efendiev Y., Hou T., Ginting V.: Multiscale finite element methods for nonlinear problems and their applications. Commun. Math. Sci. 2, 553-589 (2004) · Zbl 1083.65105
[32] Efendiev Y., Hou T.Y.: Multiscale Finite Element Methods: Theory and Applications. Springer, New York (2009) · Zbl 1163.65080
[33] Zhang H.W., Liu Y., Zhang S., Tao J., Wu J.K., Chen B.S.: Extended multiscale finite element method: its basic and applications for mechanical analysis of heterogeneous materials. Comput. Mech. 53, 659-685 (2014) · Zbl 1316.74065
[34] Liu H., Zhang H.W.: A uniform multiscale method for 3D static and dynamic analyses of heterogeneous materials. Comput. Math. Sci. 79, 159-173 (2013)
[35] Zhang H.W., Wu J.K., Fu Z.D.: Extended multiscale finite element method for elasto-plastic analysis of 2D periodic lattice truss materials. Comput. Mech. 45, 623-635 (2010) · Zbl 1398.74429
[36] Zhang H.W., Wu J.K., Lü J.: A new multiscale computational method for elasto-plastic analysis of heterogeneous materials. Comput. Mech. 49, 149-469 (2012) · Zbl 1316.74064
[37] Zhang S., Yang D.S., Zhang H.W., Zheng Y.G.: Coupling extended multiscale finite element method for thermoelastic analysis of heterogeneous multiphase materials. Comput. Struct. 121, 32-49 (2013)
[38] Ngo V.M., Ibrahimbegovic A., Brancherie D.: Model for localized failure with thermo-plastic coupling: theoretical formulation and ED-FEM implementation. Comput. Struct. 127, 2-18 (2013)
[39] Melenk J.M., Babuška I.: The partition of unity finite element method: basic theory and applications. Comput. Methods Appl. Mech. Eng. 139, 289-314 (1996) · Zbl 0881.65099
[40] Duarte C.A., Babuška I., Oden J.T.: Generalized finite element methods for three-dimensional structural mechanics problems. Comput. Struct. 77, 215-232 (2000)
[41] Strouboulis T., Copps K., Babuška I.: The generalized finite element method. Comput. Methods Appl. Mech. Eng. 190, 4081-4193 (2001) · Zbl 0997.74069
[42] Macri M., Littlefield A.: Enrichment based multiscale modeling for thermo-stress analysis of heterogeneous material. Int. J. Numer. Methods Eng. 93, 1147-1169 (2013) · Zbl 1352.74099
[43] Duarte C.A., Kim D.J.: Analysis and applications of a generalized finite element method with global-local enrichment functions. Comput. Methods Appl. Mech. Eng. 197, 487-504 (2008) · Zbl 1169.74597
[44] O’Hara P., Duarte C.A., Eason T.: Generalized finite element analysis of three-dimensional heat transfer problems exhibiting sharp thermal gradients. Comput. Methods Appl. Mech. Eng. 198, 1857-1871 (2009) · Zbl 1227.80050
[45] DeSouza Neto E.A., Peric’ D., Owen D.R.J.: Computational Methods for Plasticity: Theory and Applications. Wiley, Chichester (2008)
[46] Simo J.C., Hughes T.J.R.: Computational Inelasticity. Springer, Berlin (1998) · Zbl 0934.74003
[47] Vel S.S., Goupee A.J.: Multiscale thermoelastic analysis of random heterogeneous materials. Part I: Microstructure characterization and homogenization of material properties. Comput. Mater. Sci. 48, 22-38 (2010)
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