Instabilities of elastic bodies in motion

This thesis consists of two parts. In the first part, a simulation of contact between a two dimensional elastic object in motion in contact with a rigid obstacle under Coulumb friction is developed. Once this simulation is developed, the simulation attempts to find out what initial numerical conditions cause the object to go unstable. All results found in this first part are numerical. Based on the numerical results of this thesis it appears that the friction coefficient is the main source of instabilities occuring, but the initial velocity does impact whether or not an instability occurs to some degree as well. The second part of this thesis investigates whether or not energy is conserved during the simulations conducted in the first part of the thesis. In the first part we discover that whether or not energy is conserved has little impact on whether an instabilty occurs, but it is still desireable for energy to be conserved in a mathematical model. We show that with a slight modification to the friction condition that energy will be conserved. This is desireable as energy dissipation is usually needed to prove convergence of solutions. Unfortunately as of yet convergence of solutions cannot be proven as existance of solutions has yet to be established.