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Ruga mechanics and Ruga phase diagrams

Kyung-Suk Kim (Brown University)

Symposium in honor of Rod Clifton on the occasion of his 75th Birthday

Mon 9:00 - 10:30

Salomon 101

In recent years nano science and technology has enabled us to explore new functional properties of hierarchical ruga structures and materials through folding or wrapping thin surface layer structures with nanometer scale features. The Latin word ruga collectively denotes large-amplitude wrinkles, creases, ridges and folds. Here, a primary ruga phase diagram is introduced by carrying out a parametric study of ruga instability analysis for a neo-Hookean solid with an exponentially decaying modulus (EDM) distribution. The parametric study provides various branches of stable or unstable, supercritical or subcritical equilibrium configuration families. These branches delineate flat, wrinkle, instantaneous crease, setback crease and fold crease phases on the plane of the normalized wave number of the ruga periodicity versus the compressive strain. The parametric study further reveals that the snap-buckling crease strain converges to the Biot critical compressive strain, 45.6%, of the neo-Hookean half space, as the decay length of the elastic modulus diverges to infinity. Once the free surface of the EDM half space snaps to a stable crease bifurcation branch, the crease depth decreases, following the subcritical crease branch, as the compressive strain is reduced. The lower limit of the subcritical bifurcation converges to 35.2% as the modulus-decay parameter approaches that of a homogeneous half space. Implications the ruga phase diagram are then discussed for various applications.