Amorphous polymers in their glass transition regime : Comparison of local and macroscopic small non-linearities

The mechanical behavior of amorphous polymers in their glass transition regime is linked to dynamical heterogeneities at a nanometric scale. To describe them, we developed a finite elements method where a sample is described as a set of domains each characterized by its own relaxation time τ_i. The relaxation times are randomly distributed over the domains. We showed that this approach quantitatively describes linear relaxation measured on glassy polymers.
In this work, we focus on the onset of non-linearities where non-linear relaxation is accelerated in comparison to the linear case. We describe the non-linearity effect as a decrease in local relaxation times due to stress i.e. τ_i becomes τ_i f(σ). In a homogeneous case, the local law accelerating relaxation (f(σ)) can be identified by comparing linear and non-linear macroscopic responses. However, we show that the local and macroscopic non-linear laws are different due to dynamical heterogeneities. Comparing experiments and simulations, the local non-linear law f(σ) can be identified. We show that its shape would be as exp(σⁿ) with n larger than 1.