Scale-size dependent multi-continuum homogenization of complex bodies
Résumé
We derive a homogenized classical Cauchy continuum with an affine stress-strain relationship derived from a heterogeneous Cosserat continuum. The homogenization process encompasses intrinsic lengths related to scale-size effects. The resulting local problem exhibits asymmetry, due to the micropolar couple modulus inherited from the original microscopic Cosserat problem. To validate our results, we conducted numerical simulations using the finite element method on circularly perforated square and rectangular unit cells, highlighting the impact of the micropolar couple modulus on effective coefficients. Furthermore, we numerically show that there exists a threshold micropolar couple modulus which affects the behavior of the cell and compare the cell displacement in the presence and absence of a micropolar couple modulus.
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