Numerical simulation of polymer crystallization

We consider a mathematical model for solidification of semicrystalline polymers, describing the evolution of temperature, crystalline volume fraction, number and average size of crystals. In turn, the model couples a suitable kinetics of nonisothermal crystallization, taking into account both formation and growth of nuclei, with the thermal energy balance equation. We also present a model of secondary crystallization. The numerical approximation is performed by semiexplicit finite differences in time and finite elements in space. The fully discrete scheme amounts to solve, at any time step, a symmetric positive definite linear system preceded by a elementwise explicit computation. The computed numerical crystal structures match qualitatively the experimental ones.