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The continuous model is based on the homogenization of the discrete model (Cecchi and Sab, 2009).
The constitutive law here adopted is based on the homogenization of the material properties at the macro scale level.
To predict the aerothermal behaviour of transpiration cooled plates, a multi-scale approach based on the homogenization method of periodic material structures is presented.
In the second step, a random field model for the core material is derived, based on the homogenization results obtained in the first step.
A multi-scale approach based on the homogenization technique is then linked to the conjugate analysis in order to predict the effective thermal conductivity of the blade sections.
This model was designed based on the homogenization theory and regarded fissured loess as a composite material comprising loess matrix elements and fissure elements.
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Two different modeling techniques are presented; one is based on the asymptotic homogenization method and the other is a numerical model based on the finite element technique.
The effective viscoelastic anisotropic continuum behavior of the lattices is first computed in terms of the homogenized stiffness and viscosity matrices, based on the discrete homogenization technique.
The analytical solution is based on the asymptotic homogenization method (AHM) and for the numerical approach the finite element method (FEM) is used.
The effective viscoelastic properties obtained using the three methods based on the elastic homogenization formulas were in very good agreement with the reference solution.
The conducted analyses based on the numerical homogenization procedure employ a spatial periodically arranged in a square array representative volume element and the finite element method.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com