There Is Neither Flattening nor Self-contact or Contact with an Obstacle. Non Smooth Evolution

Abstract

In the previous chapter, it as been assumed that there are neither collision with the obstacle nor self collision. But the smooth motion can be interrupted by crushing: an eigenvalue of the stretch matrix decreases and becomes equal to $\alpha$ (think of pasta being crushed between two fingers). A discontinuity of velocity, an internal collision, occurs to avoid the eigenvalue to become lower than $\alpha$. The collision or non smooth equations of motion and the collision or non smooth constitutive laws give the new velocity allowing the motion to go on.