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Post-bifurcation analysis of a regular honeycomb structure under bi-axial loading

Ryan Elliott (University of Minnesota), Pierre Henry (Ecole Polytechnique, France)

Instability in Solids and Structures

Tue 9:00 - 10:30

Barus-Holley 190

The behavior of an infinite honeycomb structure under equi-biaxial compression was investigated. The post-bifurcation behavior of this structure has been studied using a custom computational code consisting of a bridge between a branch-following and bifurcation (BFB) code and a finite element code (FEAP). It was shown using Bloch wave theory that the first bifurcation modes of the infinite system have a periodicity of (2,2) with respect to a primitive unit cell. Thus, the bifurcation modes of a $2 \times 2$ cell were investigated, as well as the Bloch wave stability of the stable path of the first bifurcation point which showed that long wavelength instabilities exist from the bifurcation point itself. Bloch wave calculations on the principal path allowed for a better understanding of the bifurcation mechanism of the infinite system, and three paths from the first bifurcation point of a $3 \times 3$ cell were followed, so as to illustrate the complex bifurcation behavior of the infinite system.