Traditional homogenization formulations for finite volume are extended to allow for the consideration of multiple inclusions and their spatial distributions along with their corresponding individual geometric attributes. For all inclusions present in different states, a combined homogenization formulation (dubbed generalized stiffness formulation, GSF) is posed for summing the five geometric attributes of volume fraction (VF), shape or aspect ratio (AR), orientation, location (position within the domain), and number of inclusions in the domain. For verification, the solutions are compared to two literature-reported calculations of simple cases of domains containing one inclusion of specific shape and orientation in which only one attribute is varied. Once verified for simple cases, GSF stiffness solutions were run for 5040 cases of domains containing multi inclusions with various configuration combinations. These solutions were compared against 36 identical cases of 3-dimensional (3D) domains printed using acrylonitrile butadiene styrene (ABS) and experimentally tested under mechanical compression. Additionally, finite element method (FEM) simulations are run of these test structures under compression. For these test cases, effective composite stiffness values are compared for numerical solutions, experimental tests, and FEM. Relative effects on stiffness of the five inclusion geometric attributes are assessed.

Revised:

Accepted:

Published online:

Ilige S. Hage ^{1};
Ramsey F. Hamade ^{2}

@article{CRMECA_2020__348_2_113_0, author = {Ilige S. Hage and Ramsey F. Hamade}, title = {Experimentally validated combined stiffness expression for finite domain containing multiple inclusions}, journal = {Comptes Rendus. M\'ecanique}, pages = {113--135}, publisher = {Acad\'emie des sciences, Paris}, volume = {348}, number = {2}, year = {2020}, doi = {10.5802/crmeca.11}, language = {en}, }

TY - JOUR AU - Ilige S. Hage AU - Ramsey F. Hamade TI - Experimentally validated combined stiffness expression for finite domain containing multiple inclusions JO - Comptes Rendus. Mécanique PY - 2020 SP - 113 EP - 135 VL - 348 IS - 2 PB - Académie des sciences, Paris DO - 10.5802/crmeca.11 LA - en ID - CRMECA_2020__348_2_113_0 ER -

%0 Journal Article %A Ilige S. Hage %A Ramsey F. Hamade %T Experimentally validated combined stiffness expression for finite domain containing multiple inclusions %J Comptes Rendus. Mécanique %D 2020 %P 113-135 %V 348 %N 2 %I Académie des sciences, Paris %R 10.5802/crmeca.11 %G en %F CRMECA_2020__348_2_113_0

Ilige S. Hage; Ramsey F. Hamade. Experimentally validated combined stiffness expression for finite domain containing multiple inclusions. Comptes Rendus. Mécanique, Volume 348 (2020) no. 2, pp. 113-135. doi : 10.5802/crmeca.11. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.11/

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