Corrigendum to “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 (2012) 197–212]

Assumption 1 in our original paper can be replaced with the following, less stringent assumption.

[1]  S. Shtrikman,et al.  On some variational principles in anisotropic and nonhomogeneous elasticity , 1962 .

[2]  Luc Dormieux,et al.  FFT-based methods for the mechanics of composites: A general variational framework , 2010 .

[3]  J. Guermond,et al.  Theory and practice of finite elements , 2004 .

[4]  Christian Huet,et al.  Application of variational concepts to size effects in elastic heterogeneous bodies , 1990 .

[5]  K. Tanaka,et al.  Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .

[6]  Stefan Scheiner,et al.  Micromechanics of bone tissue-engineering scaffolds, based on resolution error-cleared computer tomography. , 2009, Biomaterials.

[7]  Graeme W. Milton,et al.  A fast numerical scheme for computing the response of composites using grid refinement , 1999 .

[8]  J. Willis Bounds and self-consistent estimates for the overall properties of anisotropic composites , 1977 .

[9]  Graeme W. Milton,et al.  An accelerated FFT algorithm for thermoelastic and non‐linear composites , 2008 .

[10]  A. Rau Variational Principles , 2021, Classical Mechanics.

[11]  M. Saunders,et al.  Solution of Sparse Indefinite Systems of Linear Equations , 1975 .

[12]  F. Willot,et al.  Fast Fourier Transform computations and build-up of plastic deformation in 2D, elastic-perfectly plastic, pixelwise disordered porous media , 2008, 0802.2488.

[13]  Hervé Moulinec,et al.  A computational scheme for linear and non‐linear composites with arbitrary phase contrast , 2001 .

[14]  E. Kröner Bounds for effective elastic moduli of disordered materials , 1977 .

[15]  W. Rudin Real and complex analysis , 1968 .

[16]  Zdenek P. Bazant,et al.  Identification of Viscoelastic C-S-H Behavior in Mature Cement Paste by FFT-based Homogenization Method , 2010 .

[17]  D. Jeulin,et al.  Determination of the size of the representative volume element for random composites: statistical and numerical approach , 2003 .

[18]  R. Christensen,et al.  Solutions for effective shear properties in three phase sphere and cylinder models , 1979 .

[19]  H. Moulinec,et al.  A fast numerical method for computing the linear and nonlinear mechanical properties of composites , 1994 .

[20]  Y. Benveniste,et al.  A new approach to the application of Mori-Tanaka's theory in composite materials , 1987 .

[21]  R. Hill Elastic properties of reinforced solids: some theoretical principles , 1963 .

[22]  Rudolf Zeller,et al.  Elastic Constants of Polycrystals , 1973 .

[23]  R. Christensen Two Theoretical Elasticity Micromechanics Models , 1998 .

[24]  J. Willis Lectures on Mechanics of Random Media , 2001 .

[25]  Noboru Kikuchi,et al.  Digital image-based modeling applied to the homogenization analysis of composite materials , 1997 .

[26]  C. Toulemonde,et al.  Numerical homogenization of concrete microstructures without explicit meshes , 2011 .

[27]  Jan Novák,et al.  Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients , 2010, J. Comput. Phys..