- Moving a sphere in a narrow pipe
What is the force required to move an object inside a narrow elastic pipe? The constriction by the tube induces a normal force on the sphere. In the case of solid friction, the pulling force may be simply deduced from Coulomb’s law. How does is such force modified by the addition of a lubricant? This coupled problem between elasticity and viscous flow results in a non-linear dependence of the force with the traction speed.
When a bicycle tyre is inflated the cross section of the pipe increases much more than its circumference. Can we use this effect to induce non-isotropic growth in a plate? We developed, through standard casting techniques, flat plates imbedded with a network of channels of controlled geometry. How are such plates deformed as pressure is applied to this network? Using a simplified mechanical model, 3D complex shapes can be programmed and dynamically actuated.
- Industrial and Applied Mathematics Seminar