Elastica

Buckling occurs when a thin rod of elastomer is twisted as when a rubber band is twisted. Usually these problems are solved with a lower-dimensional elastica theory.

Solution nonuniqueness

Two thin tubes of elastomer are exposed to the same boundary conditions imposed at their ends, and yet two stationary solutions result. The cross sections at top shows that one solution exhibits contact while the other does not. The left-hand-side shows values of the stress energy functional on the inside surface while the right side shows the outside

Buckling in Axial Direction

The same tube with slightly different perturbations in the initial conditions can produce buckling in the axial direction.

Dynamic simulation

An elastomer rod that is bent by 180 degrees is suddenly released. The solution shows an overshoot (due to inertia) but highly damped solution. The colors indicate sign of the horizontal velocity.

Bouncing ball

A nonrotating ball of a Mooney-Rivlin material just before impact is shown in the first frame of this dynamic calculation. Because the ball is traveling to the right and rear, the stick contact condition results in the shown rotation and deformation