Laroussi, Myriam (2002) Modelling of open-cell foams: a micro-mechanical approach. PhD thesis Structures et Matériaux, ENPC.

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Abstract

Foam behavior is complex. Depending on the constitutive solid, the resulting foam can be elastic, visco-elastic, visco-plastic or visco-elasto-plastic. However, foams have same characteristic: a plateau at low forces in the stress-strain curves (or force-displacement curves). In this study, we focus on the origin of the plateau for elastic open-cell foams which is associated with the elastic buckling of cell edges. The foam is modelled by a three dimensionnal periodic microstructure. Geometrically non linear calculations are performed. For this reason, theory of non convex homogenization is used.
First, we study large strains uniaxial compression and uniaxial deformation. Calculations are performed on periodic cells of increasing size. When the cell is not "big enough", we introduce a geometrical imperfection to initiate buckling.
Then, we apply multiaxial loadings in order determinate a yield surface in the stress space, limiting the initial elastic domain and the plateau domain. The called micro-surface is obtained by considering periodic displacement variations on different sizes of the unit cell. The resulting surface is a modified Drucker-Prager surface. We also introduce a new surface, called mixed, easier to calculate and which, in our case, is the same as the micro-surface previously obtained.
Finally, in order to validate the numerical results, an experimental study is performed on a caril foam (also call "noryl").

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