Role of dynamical heterogeneities on the viscoelastic spectrum of polymers: a stochastic continuum mechanics model

Amorphous polymers in their glass transition regime can be described as a tiling of nanometric domains. Each domain exhibits its own relaxation time which is distributed over at least 4 decades. These domains are known as dynamical heterogeneities. This article will describe the mechanics of amorphous polymers using a stochastic continuum mechanics model that includes their heterogeneous dynamics. Solving this model both by finite elements and using a self-consistent method, we find a viscoelastic relaxation spectrum quantitatively similar to that of an experimentally measured one in a polymer. We show evidence that elastic couplings between domains control the stress relaxation after a step strain and result in a narrowing of the long-time region of the viscoelastic spectrum (as compared to that of dynamical heterogeneities).