Abstract
Based on the first-order Mori–Tanaka secant model, a numerical-analytical model of elasto-plastic deformation of matrix composites is developed. The calculation results of the analytical model are "fitted" to the results of numerical simulation. The fitting parameter of the model is the ratio of the constrained equivalent strain of the matrix in the numerical model to the constrained equivalent strain of the matrix in the Mori–Tanaka model. Identification of the fitting parameter is performed using a reference stress–strain curve calculated numerically for a basic composite composition. For an arbitrary composition composite, a linear dependence of the fitting parameter on the inclusion volume fraction is used. A good agreement was obtained between the results of the calculation by the numerical-analytical model and the numerical data for isotropic and transversely isotropic composites with different contents, morphology, and contrast properties of the phases.
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References
Agoras, M., Avazmohammadi, R., Ponte Castaneda, P.: Incremental variational procedure for elasto-viscoplastic composites and application to polymer- and metal-matrix composites reinforced by spheroidal elastic particles. Int. J. Solid Struct. 97–98, 668–686 (2016). https://doi.org/10.1016/j.ijsolstr.2016.04.008
Berveiller, M., Zaoui, A.: An extension of the self-consistent scheme to plastically-flowing polycrystals. J. Mech. Phys. Solids 26, 325–344 (1978). https://doi.org/10.1016/0022-5096(78)90003-0
Tandon, G.P., Weng, G.J.: A theory of particle-reinforced plasticity. J. Appl. Mech. 55, 126–135 (1988). https://doi.org/10.1115/1.3173618
Hill, R.: A self-consistent mechanics of composite materials. J. Mech. Phys. Solids 13, 213–222 (1965). https://doi.org/10.1016/0022-5096(65)90010-4
Molinari, A., Canova, G.R., Ahzi, S.: A self consistent approach at the large deformation polycrystal viscoplasticity. Acta Metall. 35, 2983–2994 (1987). https://doi.org/10.1016/0001-6160(87)90297-5
Masson, R., Bornert, M., Suquet, P., Zaoui, A.: An affine formulation for the prediction of the effective properties of non linear composites and polycrystals. J. Mech. Phys. Solids 48(6–7), 1203–1227 (2000). https://doi.org/10.1016/S0022-5096(99)00071-X
Mori, T., Tanaka, K.: Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 21, 571–574 (1973). https://doi.org/10.1016/0001-6160(73)90064-3
Benveniste, Y.: A new approach to the application of Mori–Tanaka’s theory in composite materials. Mech. Mater. 6, 147–157 (1987). https://doi.org/10.1016/0167-6636(87)90005-6
Gilormini, P.: A critical evaluation for various nonlinear extensions of the self-consistent model. In: Proceedings of the IUTAM Symposium Held in Sevres. Paris, 29 August–1 September pp. 67–74 (1995). https://doi.org/10.1007/978-94-009-1756-9_9
Suquet, P.: Overall properties of nonlinear composites: remarks on secant and incremental formulations. In: Proceedings of the IUTAM Symposium Held in Sevres. Paris, 29 August–1 September pp. 149–156 (1995). https://doi.org/10.1007/978-94-009-1756-9_19
Hu, G.: A method of plasticity for general aligned spheroidal void of fiber-reinforced composites. Int. J. Plast. 12, 439–149 (1996). https://doi.org/10.1016/S0749-6419(96)00015-0
Buryachenko, V.: The overall elastoplastic dehavior of multiphase materials with isotropic components. Acta Mech. 119, 93–117 (1996). https://doi.org/10.1007/bf01274241
Doghri, I., Brassart, L., Adam, L., Gerard, J.-S.: A second-moment incremental formulation for the mean-field homogenization of elasto-plastic composites. Int. J. Plast. 27(3), 352–371 (2011). https://doi.org/10.1016/j.ijplas.2010.06.004
Wu, L., Noels, L., Adam, L., Doghri, I.: A combined incremental-secant mean-field homogenization scheme with per-phase residual strains for elasto-plastic composites. Int. J. Plast. 51, 80–102 (2013). https://doi.org/10.1016/j.ijplas.2013.06.006
Wu, L., Doghri, I., Noels, L.: An incremental-secant mean-field homogenization method with second statistical moments for elasto-plastic composite materials. Philos. Mag. 95, 3348–3384 (2015). https://doi.org/10.1080/14786435.2015.1087653
Kanouté, P., Boso, D.P., Chaboche, J.L., Schrefler, B.: Multiscale methods for composites: a review. Arch. Comput. Methods Eng. 16, 31–75 (2009). https://doi.org/10.1007/s11831-008-9028-8
Noels, L., Wu, L., Adam, L.: Review of homogenization methods for heterogeneous materials. In: Ulrich, P., Schmitz, G.J. (eds.) Handbook of Software Solutions for ICME, pp. 433–441. Wiley-VCH, Weinheim (2016)
Wang, Y., Huang, Z.-M.: Analytical micromechanics models for elastoplastic behavior of long fibrous composites: a critical review and comparative study. Materials 11, 1919 (2018). https://doi.org/10.3390/ma11101919
Wu, L., Adam, L., Doghri, I., Noels, L.: An incremental-secant mean-field homogenization method with second statistical moments for elasto-visco-plastic composite materials. Mech. Mater. 114, 180–200 (2017). https://doi.org/10.1016/j.mechmat.2017.08.006
Pierard, O., Gonzalez, C., Segurado, J., Llorca, J., Doghri, I.: Micromechanics of elasto-plastic materials reinforced with ellipsoidal inclusions. Int. J. Solids Struct. 44(21), 6945–6962 (2007). https://doi.org/10.1016/j.ijsolstr.2007.03.019
Brassart, L., Doghri, I., Delannay, L.: Homogenization of elasto-plastic composites coupled with a nonlinear finite element analysis of the equivalent inclusion problem. Int. J. Solid Struct. 47, 716–729 (2010). https://doi.org/10.1016/j.ijsolstr.2009.11.013
González, C., Segurado, J., Llorca, J.: Numerical simulation of elasto-plastic deformation of composites: evolution of stress microfields and implications for homogenization models. J. Mech. Phys. Solids 52(7), 1573–1593 (2004). https://doi.org/10.1016/j.jmps.2004.01.002
Ortolano, J.M., Hernandez, J.A., Oliver, J.: A comparative study on homogenization strategies for multi-scale analysis of materials. Barcelona, Spain, (2013). https://www.scipedia.com/public/Ortolano_et_al_2013a
Segurado, J.: Micromecanica computacional de materiales compuestos reforzados conpartıculas. Tesis doctoral, Madrid (2004)
Ghossein, E., Lévesque, M.: A fully automated numerical tool for a comprehensive validation of homogenization models and its application to spherical particles reinforced composites. Int. J. Solids Struct. 49(11–12), 1387–1398 (2012). https://doi.org/10.1016/j.ijsolstr.2012.02.021
Ma, H., Xu, W., Li, Y.: Random aggregate model for mesoscopic structures and mechanical analysis of fully-graded concrete. Comput. Struct. 177, 103–113 (2016). https://doi.org/10.1016/j.compstruc.2016.09.005
Wang, X., Zhang, M., Jivkov, A.P.: Computational technology for analysis of 3D meso-structure effects on damage and failure of concrete. Int. J. Solids Struct. 80, 310–333 (2016). https://doi.org/10.1016/j.ijsolstr.2015.11.018
Rekik, A., Auslender, F., Bornert, M., Zaoui, A.: Objective evaluation of linearization procedures in nonlinear homogenization: a methodology and some implications on the accuracy of micromechanical schemes. Int. J. Solid Struct. 44, 3468–3496 (2007). https://doi.org/10.1016/j.ijsolstr.2006.10.001
Matouš, K., Geers, M.G.D., Kouznetsova, V.G., Gillman, A.: A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials. J. Comput. Phys. 330(1), 192–220 (2017). https://doi.org/10.1016/j.jcp.2016.10.070
Fedotov, A.F.: Quasi-numerical model for predicting the elastic moduli of matrix composites. Compos. Struct. 308, 116679 (2023). https://doi.org/10.1016/j.compstruct.2023.116679
Llorca, J., Needleman, A., Suresh, S.: An analysis of the effects of matrix void growth on deformation and ductility in metal-ceramic composites. Acta Metal. Mater. 39, 2317–2335 (1991). https://doi.org/10.1016/0956-7151(91)90014-R
Brassart, L., Stainier, L., Doghri, I., Delannay, L.: Homogenization of elasto-(visco) plastic composites based on an incremental variational principle. Int. J. Plast. 36, 86–112 (2012). https://doi.org/10.1016/j.ijplas.2012.03.010
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Fedotov, A. A numerical-analytical model of elasto-plastic deformation of matrix composites. Acta Mech (2024). https://doi.org/10.1007/s00707-024-03918-x
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DOI: https://doi.org/10.1007/s00707-024-03918-x