Derivation of FFT numerical bounds of the effective properties of composites and polycristals

Theoretical and Applied Mechanics Letters - Tập 11 - Trang 100236 - 2021
Minh-Tan Nguyen1, Quy-Dong To1, Vincent Monchiet1
1Univ Gustave Eiffel, Univ Paris Est Creteil, CNRS, MSME UMR 8208, F-77454 Marne-la-VallÃl'e, France

Tài liệu tham khảo

Moulinec, 1994, A fast numerical method for computing the linear and nonlinear mechanical properties of composites, C. R. Acad. Sci., 318, 1417 Nemat-Nasser, 1999 Bonnet, 2007, Effective properties of elastic periodic composite media with fibers, J. Mech. Phys. Solids., 55, 881, 10.1016/j.jmps.2006.11.007 To, 2016, Explicit effective elasticity tensors of two-phase periodic composites with spherical or ellipsoidal inclusions, Int. J. Solids Struct., 94-95, 100, 10.1016/j.ijsolstr.2016.05.005 To, 2017, Overall elastic properties of composites from optimal strong contrast expansion, Int. J. Solids Struct., 120, 245, 10.1016/j.ijsolstr.2017.05.006 Brisard, 2020, FFT-based methods for the mechanics of composites: a general variational framework, Comput. Mater. Sci., 49, 663, 10.1016/j.commatsci.2010.06.009 Brisard, 2012, Combining Galerkin approximation techniques with the principle of Hashin and Shtrikman to derive a new FFT-based numerical method for the homogenization of composites, Comput. Methods Appl. Mech. Engrg., 217-220, 197, 10.1016/j.cma.2012.01.003 Mareau, 2017, Different composite voxel methods for the numerical homogenization of heterogeneous inelastic materials with FFTbased techniques, Mech. Mater., 105, 157, 10.1016/j.mechmat.2016.12.002 Kabel, 2017, The composite voxel technique for inelastic problems, Comput. Methods Appl. Mech. Engrg., 322, 396, 10.1016/j.cma.2017.04.025 Monchiet, 2015, Combining FFT methods and variational principles to compute bounds and estimates for the properties of elastic composites, Comput. Meth. Appl. Mech. Engrg., 283, 454, 10.1016/j.cma.2014.10.005 Monchiet, 2018, FFT based iterative schemes for composites conductors with non-overlapping fibers and Kapitza interface resistance, Int. J. Solids Struct., 135, 14, 10.1016/j.ijsolstr.2017.10.015 Wuttke, 2017 Moulinec, 1998, A numerical method for computing the overall response of nonlinear composites with complex microstructure, Comput. Methods. Appl. Mech. Engrg., 157, 69, 10.1016/S0045-7825(97)00218-1 Monchiet, 2012, A polarization based FFT iterative scheme for computing the effective properties of elastic composites with arbitrary contrast, Int. J. Num. Meth. Engrg., 89, 1419, 10.1002/nme.3295 Thomson, 1878, Mathematical theory of elasticity, Elasticity Encyclopedia Britannica, 7, 819 Bhattacharya, 2005, A model problem concerning recoverable strains of shape-memory polycrystals, Proc. Roy. Soc. London A, 461, 2797