A Numerical Method to Evaluate the Elastoplastic Material Properties of Fiber Reinforced Composite
The representative volume element (RVE) plays a central role in the mechanics of random heterogeneous materials with a view to predicting their effective properties. In this paper, a computational homogenization methodology, developed to determine effective linear elastic properties of composite materials, is extended to predict the effective nonlinear elastoplastic response of long fiber reinforced composite. Finite element simulations of volumes of different sizes and fiber volume fractures are performed for calculation of the overall response RVE. The dependencies of the overall stress-strain curves on the number of fibers inside the RVE are studied in the 2D cases. Volume averaged stress-strain responses are generated from RVEs and compared with the finite element calculations available in the literature at moderate and high fiber volume fractions. For these materials, the existence of an RVE is demonstrated for the sizes of RVE corresponding to 10–100 times the diameter of the fibers. In addition, the response of small size RVE is found anisotropic, whereas the average of all large ones leads to recover the isotropic material properties.
[1] Mishnaevsky Jr, Leon L. "Three-dimensional numerical testing of microstructures of particle reinforced composites." Acta Materialia 52.14 (2004): 4177-4188.
[2] González, C., J. Segurado, and J. LLorca. "Numerical simulation of elasto-plastic deformation of composites: evolution of stress microfields and implications for homogenization models." Journal of the Mechanics and Physics of Solids 52.7 (2004): 1573-1593.
[3] Pierard, O., et al. "Micromechanics of elasto-plastic materials reinforced with ellipsoidal inclusions." International Journal of Solids and Structures 44.21 (2007): 6945-6962.
[4] Tandon, G. P., and G. J. Weng. "A theory of particle-reinforced plasticity." Journal of Applied Mechanics 55.1 (1988): 126-135.
[5] Doghri, Issam, and Amine Ouaar. "Homogenization of two-phase elasto-plastic composite materials and structures: study of tangent operators, cyclic plasticity and numerical algorithms." International Journal of Solids and structures 40.7 (2003): 1681-1712.
[6] Bao, G., J. W. Hutchinson, and R. M. McMeeking. "Particle reinforcement of ductile matrices against plastic flow and creep." Acta metallurgica et materialia 39.8 (1991): 1871-1882.
[7] Delannay, Laurent, Issam Doghri, and O. Pierard. "Prediction of tension–compression cycles in multiphase steel using a modified incremental mean-field model." International Journal of Solids and Structures 44.22-23 (2007): 7291-7306.
[8] Chu, T. Y., and Zvi Hashin. "Plastic behavior of composites and porous media under isotropic stress." International Journal of Engineering Science 9.10 (1971): 971-994.
[9] Qiu, Y. P., and G. J. Weng. "A theory of plasticity for porous materials and particle-reinforced composites." Journal of Applied Mechanics 59.2 (1992): 261-268.
[10] Ju, J. W., and L. Z. Sun. "Effective elastoplastic behavior of metal matrix composites containing randomly located aligned spheroidal inhomogeneities. Part I: micromechanics-based formulation." International Journal of Solids and Structures 38.2 (2001): 183-201.
[11] Farrissey, L., et al. "Investigation of the strengthening of particulate reinforced composites using different analytical and finite element models." Computational materials science 15.1 (1999): 1-10.
[12] LLorca, J., and J. Segurado. "Three-dimensional multiparticle cell simulations of deformation and damage in sphere-reinforced composites." Materials Science and Engineering: A 365.1-2 (2004): 267-274.
[13] Sun, L. Z., and J. W. Ju. "Elastoplastic modeling of metal matrix composites containing randomly located and oriented spheroidal particles." Journal of applied mechanics 71.6 (2004): 774-785.
[14] Monetto, Ilaria, and W. J. Drugan. "A micromechanics-based nonlocal constitutive equation and minimum RVE size estimates for random elastic composites containing aligned spheroidal heterogeneities." Journal of the Mechanics and Physics of Solids 57.9 (2009): 1578-1595.
[15] Pensée, Vincent, and Q-C. He. "Generalized self-consistent estimation of the apparent isotropic elastic moduli and minimum representative volume element size of heterogeneous media." International journal of solids and structures 44.7-8 (2007): 2225-2243.
[16] Drugan, W. J., and J. R. Willis. "A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites." Journal of the Mechanics and Physics of Solids 44.4 (1996): 497-524.
[17] Bulsara, V. N., Ramesh Talreja, and J. Qu. "Damage initiation under transverse loading of unidirectional composites with arbitrarily distributed fibers." Composites science and technology 59.5 (1999): 673-682.
[18] Rakow, Joseph F., and Anthony M. Waas. "The effective isotropic moduli of random fibrous composites, platelet composites, and foamed solids." Mechanics of Advanced Materials and Structures 11.2 (2004): 151-173.
[19] Swaminathan, Shriram, Somnath Ghosh, and N. J. Pagano. "Statistically equivalent representative volume elements for unidirectional composite microstructures: Part I-Without damage." Journal of Composite Materials 40.7 (2006): 583-604.
[20] Swaminathan, Shriram, N. J. Pagano, and Somnath Ghosh. "Analysis of interfacial debonding in three-dimensional composite microstructures." Journal of engineering materials and technology 128.1 (2006): 96-106.
[21] Kanit, T., et al. "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 (2003): 3647-3679.
[22] Ranganathan, Shivakumar I., and Martin Ostoja-Starzewski. "Scaling function, anisotropy and the size of RVE in elastic random polycrystals." Journal of the Mechanics and Physics of Solids 56.9 (2008): 2773-2791.
[23] Elvin, A. A., and S. Shyam Sunder. "Microcracking due to grain boundary sliding in polycrystalline ice under uniaxial compression." Acta materialia 44.1 (1996): 43-56.
[24] Gusev, Andrei A. "Representative volume element size for elastic composites: a numerical study." Journal of the Mechanics and Physics of Solids 45.9 (1997): 1449-1459.
[25] Ostoja-Starzewski, Martin. "Material spatial randomness: From statistical to representative volume element." Probabilistic engineering mechanics 21.2 (2006): 112-132.
[26] Ren, Z-Y., and Q-S. Zheng. "A quantitative study of minimum sizes of representative volume elements of cubic polycrystals—numerical experiments." Journal of the Mechanics and Physics of Solids 50.4 (2002): 881-893.
[27] Zohdi, T. I., and P. Wriggers. "On the sensitivity of homogenized material responses at infinitesimal and finite strains." Communications in Numerical Methods in Engineering 16.9 (2000): 657-670.
[28] Salmi, Moncef, et al. "Various estimates of Representative Volume Element sizes based on a statistical analysis of the apparent behavior of random linear composites." Comptes Rendus Mécanique 340.4-5 (2012): 230-246.
[29] Soize, Christian. "Tensor-valued random fields for meso-scale stochastic model of anisotropic elastic microstructure and probabilistic analysis of representative volume element size." Probabilistic Engineering Mechanics 23.2-3 (2008): 307-323.
[30] Sab, Karam, and Boumediene Nedjar. "Periodization of random media and representative volume element size for linear composites." Comptes Rendus Mécanique 333.2 (2005): 187-195.
[31] Galli, Matteo, Joël Cugnoni, and John Botsis. "Numerical and statistical estimates of the representative volume element of elastoplastic random composites." European Journal of Mechanics-A/Solids 33 (2012): 31-38.
[32] Heinrich, C., et al. "The influence of the representative volume element (RVE) size on the homogenized response of cured fiber composites." Modelling and simulation in materials science and engineering 20.7 (2012): 075007.
[33] Salahouelhadj, A., and H. Haddadi. "Estimation of the size of the RVE for isotropic copper polycrystals by using elastic–plastic finite element homogenisation." Computational Materials Science 48.3 (2010): 447-455.
[34] Khisaeva, Z. F., and M. Ostoja-Starzewski. "On the size of RVE in finite elasticity of random composites." Journal of elasticity 85.2 (2006): 153.
[35] Pelissou, C., et al. "Determination of the size of the representative volume element for random quasi-brittle composites." International Journal of Solids and Structures 46.14-15 (2009): 2842-2855.
[36] Hill, Rodney. The mathematical theory of plasticity. Vol. 11. Oxford university press, 1998.
[37] Kachanov, Lazarʹ Markovich. Fundamentals of the Theory of Plasticity. Courier Corporation, 2004.
[38] Lubliner, Jacob. Plasticity theory. Courier Corporation, 2008.
[39] De Souza Neto, Eduardo A., Djordje Peric, and David RJ Owen. Computational methods for plasticity: theory and applications. John Wiley & Sons, 2011.
[40] Yang, Lei, et al. "A new method for generating random fibre distributions for fibre reinforced composites." Composites Science and Technology 76 (2013): 14-20.
[41] Vaughan, T. J., and C. T. McCarthy. "A combined experimental-numerical approach for generating statistically equivalent fibre distributions for high strength laminated composite materials." Composites Science and Technology 70.2 (2010): 291-297.
[42] Abaqus, Inc. "ABAQUS theory and standard user's manual." (2003).
[43] Fiedler, B., et al. "Failure behavior of an epoxy matrix under different kinds of static loading." Composites Science and Technology 61.11 (2001): 1615-1624.
[1] Mishnaevsky Jr, Leon L. "Three-dimensional numerical testing of microstructures of particle reinforced composites." Acta Materialia 52.14 (2004): 4177-4188.
[2] González, C., J. Segurado, and J. LLorca. "Numerical simulation of elasto-plastic deformation of composites: evolution of stress microfields and implications for homogenization models." Journal of the Mechanics and Physics of Solids 52.7 (2004): 1573-1593.
[3] Pierard, O., et al. "Micromechanics of elasto-plastic materials reinforced with ellipsoidal inclusions." International Journal of Solids and Structures 44.21 (2007): 6945-6962.
[4] Tandon, G. P., and G. J. Weng. "A theory of particle-reinforced plasticity." Journal of Applied Mechanics 55.1 (1988): 126-135.
[5] Doghri, Issam, and Amine Ouaar. "Homogenization of two-phase elasto-plastic composite materials and structures: study of tangent operators, cyclic plasticity and numerical algorithms." International Journal of Solids and structures 40.7 (2003): 1681-1712.
[6] Bao, G., J. W. Hutchinson, and R. M. McMeeking. "Particle reinforcement of ductile matrices against plastic flow and creep." Acta metallurgica et materialia 39.8 (1991): 1871-1882.
[7] Delannay, Laurent, Issam Doghri, and O. Pierard. "Prediction of tension–compression cycles in multiphase steel using a modified incremental mean-field model." International Journal of Solids and Structures 44.22-23 (2007): 7291-7306.
[8] Chu, T. Y., and Zvi Hashin. "Plastic behavior of composites and porous media under isotropic stress." International Journal of Engineering Science 9.10 (1971): 971-994.
[9] Qiu, Y. P., and G. J. Weng. "A theory of plasticity for porous materials and particle-reinforced composites." Journal of Applied Mechanics 59.2 (1992): 261-268.
[10] Ju, J. W., and L. Z. Sun. "Effective elastoplastic behavior of metal matrix composites containing randomly located aligned spheroidal inhomogeneities. Part I: micromechanics-based formulation." International Journal of Solids and Structures 38.2 (2001): 183-201.
[11] Farrissey, L., et al. "Investigation of the strengthening of particulate reinforced composites using different analytical and finite element models." Computational materials science 15.1 (1999): 1-10.
[12] LLorca, J., and J. Segurado. "Three-dimensional multiparticle cell simulations of deformation and damage in sphere-reinforced composites." Materials Science and Engineering: A 365.1-2 (2004): 267-274.
[13] Sun, L. Z., and J. W. Ju. "Elastoplastic modeling of metal matrix composites containing randomly located and oriented spheroidal particles." Journal of applied mechanics 71.6 (2004): 774-785.
[14] Monetto, Ilaria, and W. J. Drugan. "A micromechanics-based nonlocal constitutive equation and minimum RVE size estimates for random elastic composites containing aligned spheroidal heterogeneities." Journal of the Mechanics and Physics of Solids 57.9 (2009): 1578-1595.
[15] Pensée, Vincent, and Q-C. He. "Generalized self-consistent estimation of the apparent isotropic elastic moduli and minimum representative volume element size of heterogeneous media." International journal of solids and structures 44.7-8 (2007): 2225-2243.
[16] Drugan, W. J., and J. R. Willis. "A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites." Journal of the Mechanics and Physics of Solids 44.4 (1996): 497-524.
[17] Bulsara, V. N., Ramesh Talreja, and J. Qu. "Damage initiation under transverse loading of unidirectional composites with arbitrarily distributed fibers." Composites science and technology 59.5 (1999): 673-682.
[18] Rakow, Joseph F., and Anthony M. Waas. "The effective isotropic moduli of random fibrous composites, platelet composites, and foamed solids." Mechanics of Advanced Materials and Structures 11.2 (2004): 151-173.
[19] Swaminathan, Shriram, Somnath Ghosh, and N. J. Pagano. "Statistically equivalent representative volume elements for unidirectional composite microstructures: Part I-Without damage." Journal of Composite Materials 40.7 (2006): 583-604.
[20] Swaminathan, Shriram, N. J. Pagano, and Somnath Ghosh. "Analysis of interfacial debonding in three-dimensional composite microstructures." Journal of engineering materials and technology 128.1 (2006): 96-106.
[21] Kanit, T., et al. "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 (2003): 3647-3679.
[22] Ranganathan, Shivakumar I., and Martin Ostoja-Starzewski. "Scaling function, anisotropy and the size of RVE in elastic random polycrystals." Journal of the Mechanics and Physics of Solids 56.9 (2008): 2773-2791.
[23] Elvin, A. A., and S. Shyam Sunder. "Microcracking due to grain boundary sliding in polycrystalline ice under uniaxial compression." Acta materialia 44.1 (1996): 43-56.
[24] Gusev, Andrei A. "Representative volume element size for elastic composites: a numerical study." Journal of the Mechanics and Physics of Solids 45.9 (1997): 1449-1459.
[25] Ostoja-Starzewski, Martin. "Material spatial randomness: From statistical to representative volume element." Probabilistic engineering mechanics 21.2 (2006): 112-132.
[26] Ren, Z-Y., and Q-S. Zheng. "A quantitative study of minimum sizes of representative volume elements of cubic polycrystals—numerical experiments." Journal of the Mechanics and Physics of Solids 50.4 (2002): 881-893.
[27] Zohdi, T. I., and P. Wriggers. "On the sensitivity of homogenized material responses at infinitesimal and finite strains." Communications in Numerical Methods in Engineering 16.9 (2000): 657-670.
[28] Salmi, Moncef, et al. "Various estimates of Representative Volume Element sizes based on a statistical analysis of the apparent behavior of random linear composites." Comptes Rendus Mécanique 340.4-5 (2012): 230-246.
[29] Soize, Christian. "Tensor-valued random fields for meso-scale stochastic model of anisotropic elastic microstructure and probabilistic analysis of representative volume element size." Probabilistic Engineering Mechanics 23.2-3 (2008): 307-323.
[30] Sab, Karam, and Boumediene Nedjar. "Periodization of random media and representative volume element size for linear composites." Comptes Rendus Mécanique 333.2 (2005): 187-195.
[31] Galli, Matteo, Joël Cugnoni, and John Botsis. "Numerical and statistical estimates of the representative volume element of elastoplastic random composites." European Journal of Mechanics-A/Solids 33 (2012): 31-38.
[32] Heinrich, C., et al. "The influence of the representative volume element (RVE) size on the homogenized response of cured fiber composites." Modelling and simulation in materials science and engineering 20.7 (2012): 075007.
[33] Salahouelhadj, A., and H. Haddadi. "Estimation of the size of the RVE for isotropic copper polycrystals by using elastic–plastic finite element homogenisation." Computational Materials Science 48.3 (2010): 447-455.
[34] Khisaeva, Z. F., and M. Ostoja-Starzewski. "On the size of RVE in finite elasticity of random composites." Journal of elasticity 85.2 (2006): 153.
[35] Pelissou, C., et al. "Determination of the size of the representative volume element for random quasi-brittle composites." International Journal of Solids and Structures 46.14-15 (2009): 2842-2855.
[36] Hill, Rodney. The mathematical theory of plasticity. Vol. 11. Oxford university press, 1998.
[37] Kachanov, Lazarʹ Markovich. Fundamentals of the Theory of Plasticity. Courier Corporation, 2004.
[38] Lubliner, Jacob. Plasticity theory. Courier Corporation, 2008.
[39] De Souza Neto, Eduardo A., Djordje Peric, and David RJ Owen. Computational methods for plasticity: theory and applications. John Wiley & Sons, 2011.
[40] Yang, Lei, et al. "A new method for generating random fibre distributions for fibre reinforced composites." Composites Science and Technology 76 (2013): 14-20.
[41] Vaughan, T. J., and C. T. McCarthy. "A combined experimental-numerical approach for generating statistically equivalent fibre distributions for high strength laminated composite materials." Composites Science and Technology 70.2 (2010): 291-297.
[42] Abaqus, Inc. "ABAQUS theory and standard user's manual." (2003).
[43] Fiedler, B., et al. "Failure behavior of an epoxy matrix under different kinds of static loading." Composites Science and Technology 61.11 (2001): 1615-1624.
@article{"International Journal of Chemical, Materials and Biomolecular Sciences:78139", author = "M. Palizvan and M. H. Sadr and M. T. Abadi", title = "A Numerical Method to Evaluate the Elastoplastic Material Properties of Fiber Reinforced Composite", abstract = "The representative volume element (RVE) plays a central role in the mechanics of random heterogeneous materials with a view to predicting their effective properties. In this paper, a computational homogenization methodology, developed to determine effective linear elastic properties of composite materials, is extended to predict the effective nonlinear elastoplastic response of long fiber reinforced composite. Finite element simulations of volumes of different sizes and fiber volume fractures are performed for calculation of the overall response RVE. The dependencies of the overall stress-strain curves on the number of fibers inside the RVE are studied in the 2D cases. Volume averaged stress-strain responses are generated from RVEs and compared with the finite element calculations available in the literature at moderate and high fiber volume fractions. For these materials, the existence of an RVE is demonstrated for the sizes of RVE corresponding to 10–100 times the diameter of the fibers. In addition, the response of small size RVE is found anisotropic, whereas the average of all large ones leads to recover the isotropic material properties.
", keywords = "Homogenization, periodic boundary condition, elastoplastic properties, RVE.", volume = "12", number = "11", pages = "586-10", }
