A computational scheme for linear and non‐linear composites with arbitrary phase contrast

By J. Michel, H. Moulinec, Pierre Suquet. 2001

488 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/163268b191bd5c7391614614746dc24f260d401f

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In Computational Theory and Mathematics

In Mathematical Physics

In Mechanics of Materials

Citations in the corpus

Combining Galerkin approximation techniques with the principle of Hashin and Shtrikman to derive a new FFT-based numerical method for the homogenization of composites (2012, unknown): “For the non-consistent approach of Moulinec and Suquet [9, 10], this means that conditions (34) on the reference material are not necessary to ensure existence and uniqueness of solution to the discrete problem (35); since the Neumann iterations no longer converge [16], this solution should be compu”
Three‐dimensional finite element implementation of the nonuniform transformation field analysis (2010, methodology): “The method has been applied to two-dimensional composites with great success [16, 18, 19] using the FFT [10, 20, 21] to solve the non-linear problem on the microscopic scale.”
Continuum Models of Ductile Fracture: A Review (2010, methodology): “More accurate results may be obtained using numerical methods such as the FE method (Koplik and Needleman, 1988) or fast Fourier transform (Michel et al., 2001).”
A spectral method solution to crystal elasto-viscoplasticity at finite strains (2013, background): “For the case of isotropic elasticity , Michel et al. (2001) could show that stability is guarante ed when setting the reference stiffness A to the mean of the highest and lowest stiffness value from the domain.”
A polarization‐based FFT iterative scheme for computing the effective properties of elastic composites with arbitrary contrast (2012, unknown): “However, similarly to the original scheme [4], the number of iterations at convergence still linearly depends on the contrast (see [13]).”
A virtual laboratory using high resolution crystal plasticity simulations to determine the initial yield surface for sheet metal forming operations (2016, methodology): “However, simulation of heterogenous materials is limited by the slow convergence of the original fixpoint iterative method when applied to materials with a large contrast in local stiffness (Michel et al., 2001).”
An elasto-viscoplastic formulation based on fast Fourier transforms for the prediction of micromechanical fields in polycrystalline materials (2012, methodology): “Michel et al., 2000, 2001) as an efficient method to compute the micromechanical fields of periodic heterogeneous materials directly from an image of their microstructure.”
An assessment of the Gurson yield criterion by a computational multi‐scale approach (2009, background): “…the analysis of a microscopic representative volume element (RVE) (Hill (1963); Gurson (1977); Michel & Suquet (1992); Gărăjeu & Suquet (1997); Michel et al. (1999, 2001); Pellegrino et al. (1997, 1999)), and (b) The development and use of macroscopic constitutive models whose generally…”
Fourier‐based schemes with modified Green operator for computing the electrical response of heterogeneous media with accurate local fields (2013, methodology): “Over time, refined FFT algorithms with faster convergence properties have been devised, notably the “accelerated” [17] and “augmented-Lagrangian” [18] schemes.”