Ruga mechanics of creasing: from instantaneous to setback creases

We present mechanics of surface creasing caused by lateral compression of a nonlinear neo-Hookean solid surface, with its elastic stiffness decaying exponentially with depth. Nonlinear bifurcation stability analysis reveals that neo-Hookean solid surfaces can develop instantaneous surface creasing under compressive strains greater than 0.272 but less than 0.456. It is found that instantaneous creasing is set off when the compressive strain is large enough, and the longest-admissible perturbation wavelength relative to the decay length of the elastic modulus is shorter than a critical value. A compressive strain smaller than 0.272 can only trigger bifurcation of a stable wrinkle that can prompt a setback crease upon further compression. The minimum compressive strain required to develop setback creasing is found to be 0.174. If the relative longest-admissible perturbation wavelength is long enough, then the wrinkle can fold before it creases, and the specimen can be compressed further beyond the Biot critical strain limit of 0.456. Various bifurcation branches on a plane of normalized longest-admissible wavelength versus compressive strain delineate different phases of corrugated surface configurations to form a ruga phase diagram. The phase diagram will be useful for understating surface crease, as well as for controlling ruga structures for various applications, such as designing stretchable electronics.

JEANS MASS OF NEWTONIAN BOSE CLOUDS

The gravitational instability of free and dilute Newtonian boson clouds has been examined. For collisionless Newtonian boson clouds with a uniform unperturbated Bose gas density, it is deduced that the gravitational instability will never give rise to the formation of boson stars, but only black holes; however if the unperturbated density, in the neighbourhood of the perturbation, has a scale length equal to or smaller than the perturbation wavelength, the formation of free Newtonian boson stars could also be possible. For dilute Newtonian boson clouds it is shown that the gravitational instability can lead the cloud to condense into boson stars of different masses but identical radii, in agreement with studies about equilibrium configurations of dilute Newtonian boson stars. The galactic distribution of these Newtonian boson stars, and hence, the average distance among them is also discussed.