zbMATH — the first resource for mathematics

An accelerated FFT algorithm for thermoelastic and nonlinear composites. (English) Zbl 1195.74302
Summary: A fast numerical algorithm to compute the local and overall responses of nonlinear composite materials is developed. This alternative formulation allows us to improve the convergence of the existing method of e.g. H. Moulinec and P. Suquet [Comput. Methods Appl. Mech. Eng. 157, No. 1–2, 69–94 (1998; Zbl 0954.74079)]. In the present method, a nonlinear elastic (or conducting) material is replaced by infinitely many locally linear thermoelastic materials with moduli that depend on the values of the local fields. This makes it possible to use the advantages of an algorithm developed by D.J. Eyre and G.W. Milton [Eur. Phys. J. Appl. Phys. 6, No. 1, 41–47 (1999)], which has faster convergence. The method is applied to compute the local fields as well as the effective response of nonlinear conducting and elastic periodic composites.

74S30 Other numerical methods in solid mechanics (MSC2010)
74E30 Composite and mixture properties
74F05 Thermal effects in solid mechanics
Full Text: DOI
[1] Davis LC. Calculating the elastic properties of composite materials. Advanced Composites: Design, Materials and Processing Technologies. Proceedings of the 8th Annual ASM/ESD Advanced Composites Conference, Chicago, IL, 1992; 267-272.
[2] Helsing, Electrostatics of anisotropic inclusions in anisotropic media, Journal of Applied Physics 78 pp 2498– (1995) · Zbl 0846.65080
[3] Greengard, A fast algorithm for particle simulations, Journal of Computational Physics 73 pp 325– (1987) · Zbl 0629.65005
[4] Helsing, Duality relations, correspondences and numerical results for planar elastic composites, Journal of the Mechanics and Physics of Solids 45 pp 565– (1997) · Zbl 0969.74567
[5] Nunan, Effective elasticity tensor of a periodic composite, Journal of the Mechanics and Physics of Solids 32 pp 259– (1984) · Zbl 0549.73003
[6] Helsing, Fast and accurate numerical solution to an elastostatic problem involving ten thousand randomly oriented cracks, International Journal of Fracture 100 pp 321– (2000)
[7] Moulinec, A fast numerical method for computing the linear and non-linear properties of composites, Comptes Rendus des Séances de l’Académie des Sciences, Série II 318 pp 1417– (1994)
[8] Moulinec, A numerical method for computing the overall response of non-linear composites with complex microstructure, Computer Methods in Applied Mechanics and Engineering 157 (1-2) pp 69– (1998) · Zbl 0954.74079
[9] Eyre, A fast numerical scheme for computing the response of composites using grid refinement, The European Physical Journal-Applied Physics 6 (1) pp 41– (1999)
[10] Michel, A computational method based on augmented Lagrangians and fast Fourier transforms for composites with high contrast, Computer Modeling in Engineering and Sciences 1 (2) pp 79– (2000)
[11] Michel, A computational scheme for linear and nonlinear composites with arbitrary phase contrast, International Journal for Numerical Methods in Engineering 52 (1-2) pp 139– (2001)
[12] Milton, The Theory of Composites (2002) · Zbl 0993.74002
[13] Ponte Castañeda, Advances in Applied Mechanics 34 pp 171– (1998)
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.