Albion College

Mathematics and Computer Science

Mathematics and Computer Science

COLLOQUIUM

Unusual Behavior in Rubber Cubes

Darren E. Mason

In this talk we will consider the mathematical problem associated with special linear deformations of an
incompressible and nonlinear elastic cube. We will discover that the problem admits a wide variety of
different solutions, depending on the magnitude and direction of external isotropic forces. To understand why
certain solutions are preferred by nature, we will then study an associated energy minimization problem that
leads to a selection criterion to determine the optimal deformed state of the cube. Finally, we will connect
the mathematical appearences of these multiple solutions, natural and mathematical stability, and the fundamentals
of bifurcation theory.