Issue 49

M. Hamdi et alii, Frattura ed Integrità Strutturale, 49 (2019) 321-330; DOI: 10.3221/IGF-ESIS.49.32 330 The following conclusions can be drawn from the above-mentioned facts: 1. The fidelity of MSG, when it is applied to the modeling of other structures (e.g., beams, plates, and shells), can be similarly evaluated; 2. Given its homogenization capability, MSG can be applied to structural design, analysis, and optimization, as well as uncertainty quantification of composite effective properties; 3. Given its dehomogenization capability, MSG can be applied to the modeling of damage, failure, and inter-face debonding in composite structures. R EFERENCES [1] Yu, W., Tang, T. (2007). A variational asymptotic micromechanics model for predicting thermoelastic properties of heterogeneous materials. Int J Solids Struct 44, pp. 7510-7525. DOI: 10.1016/j.ijsolstr.2007.04.026. [2] Hill, R. (1952). the elastic behaviour of a crystalline aggregate. Proc. Phys. Soc. A 65, pp. 349-354. DOI: 10.1088/0370-1298/65/5/307. [3] Hill, R. (1965). A self-consistent mechanics of composite materials. J Mech Phys Solids 13, pp. 213-222. DOI: 10.1016/0022-5096(65)90010-4. [4] Hashin, Z., Shtrikman, S. (1963). A variational approach to the theory of the elastic behaviour of multiphase materials. J Mech Phys Solids 11, pp. 127-140. DOI: 10.1016/0022-5096 (63)90060-7 [5] Milton, G. (1981) Bounds on the electromagnetic elastic, and other properties of two-component composites. Phys. Rev. Lett. 46, pp. 542-545. DOI: 10.1103/PhysRevLett.46.542 [6] Banerjee, B., Adams, D.O. (2004). on predicting the effective elastic properties of polymer bonded explosives using the recursive cell method. Int J Solids Struct 41, pp. 481-509. DOI: 10.1016/j.ijsolstr.2003.09.016. [7] Bensoussan, A., Lions, J., Papanicolaou, G. (1978). Asymptotic analysis for periodic structures. Amsterdam, North- Holland, Newyork. DOI: 10.1090/chel/374. [8] Murakami, H., Toledano, A. (1990). A high-order mixture homogenization of bi-laminated composites. J. Appl. Mech. 57, pp. 388-397. DOI: 10.1115/1.2892002. [9] Hollister, S.J., Kikuchi, N. (1992). A comparison of homogenization and standard mechanics analyses for periodic porous composites. Comput Mech 10, pp. 73-95. DOI: 10.1007/BF00369853. [10] Aboudi, J. (1986). Elastoplasticity theory for composite materials. Solid Mechanics Archives 11, pp. 141-183. DOI: 10.1016/0749-6419(88)90016-2 [11] Aboudi, J. (2004) The generalized method of cells and high-fidelity generalized method of cells micromechanical models-a review. Mech Adv Mater Struc 11, pp. 329-366. DOI: 10.1080/15376490490451543. [12] Bednarcyk, B.A., Arnold, S.M. (2002). MAC/GMC 4.0 User’s Manual Keywords Manual. https://www.researchgate.net/publication/24299187_MACGMC_40_User 's_Manual_Keywords_Manual. [13] Bednarcyk, B., Arnold, S. (2002). MAC/GMC 4.0 User’s Manual Example Problem Manual. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20030015411.pdf. [14] Williams, T., Yu, W., Aboudi, J., et al. (2007) A critical evaluation of the predictive capabilities of various advanced micromechanics models. Proceedings of the 48th Structures, Structural Dynamics, and Materials Conference, Hawaii. DOI: 10.2514/6.2007-2084. [15] Yu, W. (2016) A unified theory for constitutive modeling of composites. J Mech Mater Struct 11, pp. 379-411. DOI: 10.2140/jomms.2016.11.379 [16] Sun, C.T., Vaidya, R.S. (1996) Prediction of composite properties from a representative volume element. Compos Sci Technol 56, pp. 171179. DOI: 10.1016/0266-3538(95)00141-7 [17] Berdichevsky, V. (2009) Variational Principles of Continuum Mechanics. Springer, Berlin. DOI: 10.1007/978-3-540-88469-9. [18] Pahr, D., Arnold, S. (2002) The applicability of the generalized method of cells for analyzing discontinuously reinforced composites. Compos Part B Eng 33, pp. 153-170. DOI: 10.1016/S1359-8368(01)00061-0. [19] Massart, T.J., Mercatoris, B.C.N., Piezel, B., et al. (2011) Multiscale modelling of heterogeneous shell structures. Computer Assisted Mechanics and Engineering Sciences 18, pp. 53-71. DOI: 10.1108/02644400510603050. [20] Sevostianov, I., Rodriguez-Ramos, R., Guinovart-Diaz, .R, et al. (2012) Connections between different models describing imperfect interfaces in periodic fiber-reinforced composites. Int J Solids Struct 49, pp. 1518-1525. DOI: 10.1016/j.ijsolstr.2012.02.028.