Morphology-dependent Hashin–Shtrikman bounds on the effective properties of stress-gradient materials

6.. arbitrarily small, this fictitious layer is also stiffer than the matrix and the inclusions. In other words, the reference medium is softer than all phases in the composite, and

In this paper, we have presented a mathematical analysis of two FFT-based schemes for the numerical homogenization of composites within the framework of linear elasticity: the

► No admissibility condition for the trial stress-polarization fields ► Can provide bounds or estimates of the effective properties ► Span the whole range of homogenization

The relation between the Talbot–Willis and the Ponte Castañeda methods has been investigated in [15] : for two-phase composites with perfectly conducting inclusions, the two

The recently developed variational framework for polarization methods in nanocomposites is applied to the determination of a lower-bound on the shear modulus of a nanocomposite

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

In this paper, we have presented an attempt at improving the classical bounds of Hashin and Shtrikman [1], by considering enriched trial fields which incorporate non-trivial

In other words, we get the surprising result that the enriched trial field ( 15 ) does not improve the classical Hashin and Shtrikman bounds on the e ffective elastic properties..