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Enforcing Boundary Conditions in Micro-Macro Transition for Second Order Continuum

Łukasz Kaczmarczyk1

e-mail:, Institute of Computer Methods in Civil Engineering, Cracow University of Technology, Poland.

Computers, Materials & Continua 2006, 4(2), 55-62.


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).


Cite This Article

. Kaczmarczyk, "Enforcing boundary conditions in micro-macro transition for second order continuum," Computers, Materials & Continua, vol. 4, no.2, pp. 55–62, 2006.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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