A mechanical structure can be damaged suddenly, for instance by a collision or an explosion. It can be smoothly and progressively damaged by mechanical or chemical actions. We address the two problems considering a simple structure: a beam.
1. Smooth motion and damage. We derive the theory based on the principle of virtual power and on convenient constitutive laws.
2. Non smooth motion. Collisions. The beam is collided by a heavy steel ball. We build a theory to predict the motion after the collision, i.e., to compute the velocity field of the beam after the collision. The equations result from the principle of virtual work, the definition of convenient percussions (i.e., internal forces) and the derivations of constitutive laws.
Only basic continuum mechanics notions are needed to follow the mini-course which is intended to be interactive. Numerical applications are possible.