An improved mean-field homogenization model for the three-dimensional elastic properties of masonry

3D analytical and numerical upper‐bound homogenization approaches to the in‐plane strength domain of a running‐bond masonry wall

“…The static approach of yield design consists in directly applying this definition, while the kinematic approach relies on the introduction of the maximum resisting work 𝑊 𝑟𝑚 in a virtual velocity field 𝑈: ∀𝑈 𝐶.𝐴. 𝐷 ∶ 𝑊 𝑚𝑟 (𝑈) = ∫ Ω 𝜋(𝑑, 𝜉) dΩ + ∫ Σ 𝜋(𝑉, 𝑛, 𝜉) d𝑆 (12) where 𝑉 is the velocity jump across a discontinuity surface Σ along the unit normal 𝑛. The support function 𝜋 depends on the considered material, thus on 𝜉.…”

“…Another, and maybe the most rigorous, way to take into account the material anisotropy due to the presence of joints is to resort to multiscale methods, which are often used for masonry. One can cite, for instance, Anthoine, 8 Cecchi, and Sab [9][10][11] or recently Zhou et al 12 for the analytical derivation of elastic models, Mistler et al 13 or Donval et al 14 for the numerical derivation of the same elastic properties, Pegon and Anthoine, 15 Sacco 16 or Drougkas et al 17 for non-linear homogenisation relying on a damage model, and Zucchini and Lourenço 18,19 for a plasticity (in compression)-damage (in traction) model. The latter models, taking damage behaviour into account, may appear as the most performing constitutive models, as they provide a better assessment of the quasi-brittle behaviour of masonry.…”

“…Another, and maybe the most rigorous, way to take into account the material anisotropy due to the presence of joints is to resort to multiscale methods, which are often used for masonry. One can cite, for instance, Anthoine, 8 Cecchi, and Sab 9–11 or recently Zhou et al 12 . for the analytical derivation of elastic models, Mistler et al 13 .…”

Accounting for spatial distribution in mean-field homogenization of particulate composites

“…While MT and FF are widely used in the literature with established parameter selection methods, the situation is somewhat distinct for the classical PCW, which is also frequently employed, and for IDD. The selection of cell parameters from a given microstructure remains an open question, despite their use in previous studies [18,11,19,20,21].…”

A multiscale homogenization iterative algorithm of 2D orthogonal prepreg carbon/aramid/epoxy woven-ply

“…Vfm here can also be expressed by equation (17). Similar to ECPL-1, the expression of ECPL-2 can also be obtained from equations 17 and 18 by exchanging superscript “wa” and “we.” Meanwhile, the mesoscale homogenized stress and strain can be written based on the mean field homogenization theory 26,53 …”