PSI - Issue 37

Anastopoulos G. Stylianos et al. / Procedia Structural Integrity 37 (2022) 485–491 Anastopoulos G Stylianos et al/ Structural Integrity Procedia 00 (2019) 000 – 000

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target effective modulus calculated effective modulus of elasticity

optimization volume fraction experimental volume fraction

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12 CNTs volume fraction [ o / oo ] 13 14 15

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Effective modulus of elasticity [MPa]

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Number of iterations [-]

Number of iterations [-]

Fig. 6 (a) Effective modulus of elasticity versus number of iterations per optimization case (b) CNTs volume fraction numbers of iterations per optimization case. References Anastopoulos, S., Givannaki, F., Papanikos, P., Metaxa, Z., & Alexopoulos, N. 2020. Calculation of a composite material’s modulus of elasticity: comparison of results using fixed angles orientation and RVE with those using random orientation tensor and multi-step homogenization. v.28(Procedia Structural Integrity), pp. 2132-2141. Berger, H., Kari, S., Gabbert, U., Ramos, R., Castillero, J., & Diaz, R. 2007. Evaluation of effective material properties of randomly distributed short cylindrical fiber composites using a numerical homogenization technique. Journal of Mechanics of Materials and Structures(v. 2, No. 8), pp. 1561-1570. Djebara, Y., Moumen, A., Kanit, T., Madani, S., & Imad, A. 2016. Modeling of the effect of particles size, particles distribution and particles number on mechanical properties of polymer-clay nano-composites: Numerical homogenization versus experimental results. Composites Part B: Engineering, v.86, pp. 135-142. Documentation, Abaqus. 2017. https://abaqus-docs.mit.edu/2017/English/SIMACAEMATRefMap/simamat-c-meanfieldhomogenization.htm. Metaxa, Z. 2012. Mechanical Behaviour and Durability of advanced cement based materials, Ph.D Thesis. Mori, T., & Tanaka, K. 1973. Average Stress in the Matrix and Average Elastic Energy of Materials with Misfitting Inclusions. Acta Metall, vol. 21, pp. 571 – 574. Reuss, A. 1929. Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitäts bedingung für Einkristalle. Z.angew. Math.Mech, vol. 9, pp. 49-58. Voigt, W. 1889. Über die Beziehung zwischen den beiden Elastizitäts konstanten isotroper Körper. vol. 38, pp. 573-587. Wenya Shu, Ilinca Stanciulescu. 2020. Multiscale homogenization method for the prediction of elastic properties of fiber-reinforced composites. International Journal of Solids and Structures(v. 203), pp. 249-263. Yu , M.-F., Lourie, O., Dyer, M., Moloni, K., Kelly, T., & Ruoff, R. 2000. Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes Under Tensile Load. Science, v.287(Issue 5453), pp. 637-640. Zengrui Song, Xianghe Penga, Shan Tang, Tao Fua. 2020. A homogenization scheme for elastoplastic composites using concept of Mori-Tanaka method and average deformation power rate density. International Journal of Plasticity, v. 125.