Assessment of models and methods for pressurized spherical composites. (English) Zbl 1391.74048

Summary: The elastic properties of a spherical heterogeneous structure with isotropic periodic components is analyzed and a methodology is developed using the two-scale asymptotic homogenization method (AHM) and spherical assemblage model (SAM). The effective coefficients are obtained via AHM for two different composites: (a) composite with perfect contact between two layers distributed periodically along the radial axis; and (b) considering a thin elastic interphase between the layers (intermediate layer) distributed periodically along the radial axis under perfect contact. As a result, the derived overall properties via AHM for homogeneous spherical structure have transversely isotropic behavior. Consequently, the homogenized problem is solved. Using SAM, the analytical exact solutions for appropriate boundary value problems are provided for different number of layers for the cases (a) and (b) in the spherical composite. The numerical results for the displacements, radial and circumferential stresses for both methods are compared considering a spherical composite material loaded by an inside pressure with the two cases of contact conditions between the layers (a) and (b).


74E30 Composite and mixture properties
74Q05 Homogenization in equilibrium problems of solid mechanics
Full Text: DOI HAL


[1] [1] Reddy, J. Mechanics of laminated composite plates and shells. Theory and analysis. Boca Raton, FL: CRC Press, 2004. · Zbl 1075.74001
[2] [2] Strek, T, Jopek, H, Maruszewski, B. Computational analysis of sandwich- structured composites with an auxetic phase. Physics Status Solidi B 2014; 251: 354-366.
[3] [3] Fessel, G, Broughton, J, Fellows, N. Evaluation of different lap-shear joint geometries for automotive applications. Int J Adhesion Adhesives 2007; 27: 574-583.
[4] [4] Sapuan, S, Maleque, MA, Hameedullah, M. A note on the conceptual design of polymeric composite automotive bumper system. J Mater Process Technol 2005; 159: 145-151.
[5] [5] Fillep, S, Mergheim, P, Steinmann, P. Computational modelling and homogenization of technical textiles. Eng Struct 2013; 50: 68-73. · Zbl 1311.74100
[6] [6] Peng, X, Cao, J. A dual homogenization and finite element approach for material characterization of textile composites. Composite B 2002; 33: 45-56.
[7] [7] Murakami, M, Kondoh, M, Iwai, Y. Measurement of aerodynamic forces and flow field of a soccer ball in a wind tunnel for knuckle effect. Procedia Engineering 2010; 2: 2467-2472.
[8] [8] Cross, R. Physics of Baseball and Softball. New York: Springer, 2011.
[9] [9] Nathan, A. The effect of spin on the flight of a baseball. Am Assoc Phys Teachers 2008; 76: 119-124.
[10] [10] Hashin, Z. Thin interphase imperfect interface in elasticity with application to coated fiber composites. J Mech Physics Solids 2002; 50: 2509-2537. · Zbl 1080.74006
[11] [11] Vasilenko, A, Emel’yanov, I, Kuznetsov, V. Stress analysis of laminated shells of revolution with an imperfect interlayer contact. Int Appl Mech 2001; 37: 662-669. · Zbl 1010.74574
[12] [12] Aboudi, J. Damage in composites-modeling of imperfect bonding. Composites Sci Technol 1987; 28: 103-128.
[13] [13] Rizzoni, R, Lebon, F. Imperfect interfaces as asymptotic models of thin curved elastic adhesive interphase. Mech Res Commun 2013; 51: 39-50.
[14] [14] Chen, YC, Rajagopal, KR, Wheeler, L. Homogenization and global responses of inhomogeneous spherical nonlinear elastic shells. J Elasticity 2006; 82: 193-214. · Zbl 1094.74046
[15] [15] Lutoborski, A. Homogenization of linear elastic shells. J Elasticity 1985; 15: 69-87. · Zbl 0558.73055
[16] [16] Saha, G, Kalamkarov, AL, Georgiades, AV. Asymptotic homogenization modeling and analysis of the effective properties of smart composite reinforced and sandwich shells. Int J Mech Sci 2007; 49: 138-150.
[17] [17] Ding, H, Chen, W, Liangchi, Z. Solid Mechanics and its applications: Elasticity of Transversely Isotropic materials. Dordrecht: Springer, 2006. · Zbl 1101.74001
[18] [18] Frydmann, M . Determinations of the dynamics elastic constants of a transverse isotropic rock based on borehole dipole sonic anisotropy in deviated wells. In Rio Oil and Gas Expo and Conference 2010 Proceedings, vol. 1, pp. 1-10.
[19] [19] Weiss, JA, Maker, BN, Govindjee, S. Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comput Meth Appl Mech Eng 1996; 135: 107-128. · Zbl 0893.73071
[20] [20] Yoon, YJ, Yang, G, Cowin, C. Estimation of the effective transversely isotropic elastic constants of a material from known values of the material’s orthotropic elastic constants. Biomech Model Mechanobiol 2002; 1: 83-93.
[21] [21] Pobedrya, B. Mechanics of Composite Materials. Moscow: Moscow State University Press, 1984.
[22] [22] Tsalis, D, Chatzigeorgiou, G, Charalambakis, N. Homogenization of structures with generalized periodicity. Composites B 2012; 43: 2495-2512.
[23] [23] Ciarlet, PG. Mathematical Elasticity: Theory of shells, vol. III. Amsterdam: Elsevier Science B. V., 2000.
[24] [24] Lavrentyev, I, Rokhlin, S. Ultrasonic spectroscopy of imperfect contact interfaces between a layer and two solids. J Acoust Soc Am 1998; 103: 657-664.
[25] [25] Bakhvalov, N, Panasenko, G. Homogenisation: Averaging Processes in Periodic Media. Moscow: Mathematics and its Application (Soviet Series), 1989. · Zbl 0692.73012
[26] [26] Cioranescu, D, Donato, P. An Introduction to Homogenization. New York: Oxford University Press, 1999. · Zbl 0939.35001
[27] [27] Guinovart-Sanjuán, D, Rodríguez-Ramos, R, Guinovart-Díaz, R. Effective properties of regular elastic laminated shell composite. Composites B 2016; 87: 12-20.
[28] [28] Love, A. A Treatise on the Mathematical Theory of Elasticity. New York: Dover Publications, 1944. · Zbl 0063.03651
[29] [29] Bufler, H. The arbitrarily and the periodically laminated elastic hollow sphere: exact solutions and homogenization. Arch Appl Mech 1998; 68: 579-588. · Zbl 0927.74015
[30] [30] Ibrahim, A, Ryu, Y, Saidpour, M. Stress analysis of thin-walled pressure vessels. Modern Mech Eng 2015; 5: 1-9.
[31] [31] Hearn, E. Mechanics of Materials 1. London: Butterworth Heinemann, 2000.
[32] [32] Briane, M, Canar-Eddine, M. Homogenization of two-dimensional elasticity problems with very stiff coefficients. J Math Pures Appl 2007; 88(6): 483-505. · Zbl 1134.35010
[33] [33] Adrianov, I, Bolshkov, V, Danishevs’kyy, V. Higher order asymptotic homogenization and wave propagation in periodic composite materials. Proc R Soc A 2008; 464: 1181-1201.
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.