×

Numerical bounds for elastic properties of unidirectional non-overlapping fiber reinforced materials. (English) Zbl 1473.74113

Summary: Throughout this work, the influence of microstructures of non-overlapping aligned fiber reinforced composites on macroscopic elastic properties has been quantified with numerical homogenization on FEM simulations. New bounds that frame bulk and shear moduli of any equilibrium system were established. The corresponding microstructures for lower and upper bounds were found to be respectively a Percus-Yevick distribution of fibers and specific configurations of packed fibers. The radial distribution function has proven to be the best second order correlation to describe these fiber spatial distributions that were built with simulated annealing. The new numerical bounds established in this paper are tighter than existing third order ones.

MSC:

74Q20 Bounds on effective properties in solid mechanics
74Q15 Effective constitutive equations in solid mechanics
74Q05 Homogenization in equilibrium problems of solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Beicha, D.; Kanit, T.; Brunet, Y.; Imad, A.; El Moumen, A.; Khelfaoui, Y., Effective transverse elastic properties of unidirectional fiber reinforced composites, Mech. Mater., 102, 47-53 (2016)
[2] Beran, M. J., Use of the vibrational approach to determine bounds for the effective permittivity in random media, Il Nuovo Cimento, XXXVIII (1965), N. 2
[3] Beran, M. J.; Molyneux, J., Use of classical variational principles to determine bounds for the effective bulk modulus in heterogeneous media, Q. Appl. Math., 24, 2, 107-118 (1966) · Zbl 0139.42601
[4] Beran, M. J.; Silnutzer, R., Electrical, thermal and magnetic properties of fiber reinforced materials, J. Compos. Mater., 5, 24 (1971)
[5] Berkache, K.; Deogekar, S.; Goda, I.; Picu, R. C.; Ganghoffer, J.-F., Homogenized elastic response of random fiber networks based on strain gradient continuum models, Math. Mech. Solids, 24, 12, 3880-3896 (2019) · Zbl 07273398
[6] Bertsimas, D.; Tsitsilis, J., Simulated annealing, Stat. Sci., 8, 1, 10-15 (1993)
[7] Bravo, S. Y.; Santos, A., A heuristic radial distribution function for hard disks, J. Chem. Phys., 99 (1993), No. 3
[8] Brown, W. F., Solid mixture permittivities, J. Chem. Phys., 23 (1955), N. 8
[9] Elsayed, M. A.; McCoy, J. J., Effective physical properties of composite materials, J. Compos. Mater., 7, 466 (1973)
[10] Erchiqui, F., Application of genetic and simulated annealing algorithms for optimization of infrared heating stage in thermoforming process, Appl. Therm. Eng., 128, 1263-1272 (2017)
[11] Hansen, J. P.; McDonald, I. R., Theory of Simple Liquids (1987)
[12] 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
[13] Joslin, C. G.; Stell, G., Bounds on the properties of fiber-reinforced composites, J. Appl. Phys., 60, 5 (1986)
[14] Kanit, T.; Forest, S.; Galliet, I.; Mounoury, V.; Jeulin, D., Determination of the size of the representative volume element for random composites: statistical and numerical approach, Int. J. Solids Struct., 40, 3647-3679 (2003) · Zbl 1038.74605
[15] Kirkpatrick, S.; Gellat, C. D.; Vecchi, M. P., Optimization by simulated annealing, 1983, Sci., New Ser., 220, 671-680 (1983), No. 4598 · Zbl 1225.90162
[16] Lakhal, L.; Brunet, Y.; Kanit, T., Evaluation of second-order correlations adjusted with simulated annealing on physical properties of unidirectional non-overlapping reinforced materials (UD Composites), Int. J. Mod. Phys. C, 30 (2019), Nos. 2 & 3
[17] Lippmann, N.; Steinkopff, Th; Schmauder, S.; Gumbsch, P., 3D-finite-element-modelling of microstructures with the method of multiphase elements, Comput. Mater. Sci., 9, 28-35 (1997)
[18] McCoy, J. J., Recent Advances in Engineering Sciences, vol. 5, 235 (1970), Gordon and Breach: Gordon and Breach New York
[19] Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. N.; Tellet, A. H., Equation of state calculations by fast computing machines, J. Chem. Phys., 21, 6 (1953) · Zbl 1431.65006
[20] Miller, M. N., Bounds for effective bulk modulus of heterogeneous materials, J. Math. Phys., 10, 11, 2005-2013 (1969), 1969
[21] Miller, M. N.; Torquato, S., Improved bounds on elastic and transport properties of fiber-reinforced composites: effect of polydispersivity in fiber radius, J. Appl. Phys., 69, 4 (1991)
[22] Milton, G. W., Bounds on the Elastic and Transport properties of two-component composites, J. Mech. Phys. Solids, 30, 3, 177-191 (1982) · Zbl 0486.73063
[23] Rintoul, M.; Torquato, S., Reconstruction of the structure of dispersions, J. Colloid Interface Sci., 186, 467-476 (1997)
[24] Torquato, S., Statistical description of microstructures, Annu. Rev. Mater. Res., 32, 77-111 (2002), 2002
[25] Torquato, S.; Beasley, J. D., Effective properties of fiber-reinforced materials: II-Bounds of the effective elastic moduli of dispersions of fully penetrable cylinders, Int. J. Eng. Sci., 24, 3, 435-447 (1986)
[26] Torquato, S.; Lado, F., Bounds on the effective transport and elastic properties of a random array of cylindrical fibers in a matrix, J. Appl. Mech., 55, 347-353 (1988)
[27] Walpole, L. J., On bounds for the overall elastic moduli of inhomogeneous systems—II, J. Mech. Phys. Solids, 14, 5, 289-301 (1966) · Zbl 0139.18701
[28] Widom, B. J., Random sequential addition of hard spheres to a volume, J. Chem. Phys., 44, 3888-3894 (1966)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.