Stochastic Approach to Plastic Deformation of Polymers

Department of Mathematics and Computer Science Master of Science in Industrial and Applied Mathematics Stochastic Approach to Plastic Deformation of Polymers by Saeed Masroor Behind the plastic deformation in polymers lies a thermally activated process. This process consists of breakage of (inter-molecular) bonds and slippage of polymer chains on each other. The well-known Eyring model provides a heuristic picture of transition from elastic to plastic regime. In this thesis a stochastic version of the Eyring model is constructed in order to improve the classical model. The volume of the sample under deformation comes into play and affects the amplitude of the noise. Then a particle systems approach is proposed as a possible way of treating the problem. Possible challenges are discussed as well as the need for a more rigorous understanding of the process since one observes large fluctuation of the noise near the yield point. In this respect, a toy model has been constructed as a discrete analogue of plastic deformation. For this model numerical simulations are given and continuum limits are taken to finally obtain a stochastic differential equation. The stochastic Eyring model and the limit of the discrete system are compared and it is emphasized that the stochastic description of the system in terms of Fokker-Planck equation or the corresponding stochastic differential equation is valid only in small amplitude noise regime.