Study of stochastic aspects in the modeling of the strain-induced crystallization in unfilled polymers

Abstract

The present contribution deals with the mechanical modeling of the crystallization of unfilled polymers under consideration of stochastic aspects of the process. The framework applied is thermodynamically consistent. The model involves the diameter of crystalline regions and the distance between these regions as internal variables. The necessary evolution equations are based on the assumptions for the effective free energy and the dissipation potential of a control volume. A distribution function is introduced to express the expectation value of relevant quantities. Furthermore, the numerical implementation of probability integrals is shown. The proposed concepts are of general nature and can be taken as a basis for the modeling of similar stochastic processes involving the evolution of the internal microstructure.