In recent years the multiscale computational
homogenisation has been extensively developed. Such
micro-macro modelling does not require any constitutive
assumptions at the macro-level. The multi-scale computational
homogenisation has also been extended for the
second order continuum at the macro level Kouznetsova
V.G., Geers M.G.D., and Brekelmans V.A.M (2004). The
second-order framework is based on incorporation of the
gradient of macroscopic deformation in micro to macro
multiscale transition. The introduction of the secondorder
continuum at macro-scale takes into account the
size effect and gives more accurate results in case of
insufficient scale separation. The general framework
of computational homogenisation has been presented in
Kouznetsova V.G (2002).
. Kaczmarczyk, "Enforcing boundary conditions in micro-macro transition for second order continuum," Computers, Materials & Continua, vol. 4, no.2, pp. 55–62, 2006. https://doi.org/10.3970/cmc.2006.004.055
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