Simulation of strain-induced anisotropy for polymers with weighting functions

The alignment of polymer chains is a well-known microstructural evolution effect due to straining of polymers. This has a drastic influence on the macroscopic properties of the initially isotropic material, such as a pronounced strength in the loading direction of stretched films. For modeling the effect of strain-induced anisotropy, a macroscopic constitutive model is developed in this paper. Within a thermodynamic framework, an additive decomposition of the logarithmic Hencky strain tensor into elastic and inelastic parts is used to formulate the constitutive equations. As a key idea, weighting functions are introduced to represent a strain-softening/hardening effect to account for induced anisotropy. These functions represent the ratio between the total strain rate (representing the actual loading direction) and a structural tensor (representing the stretched polymer chains). In this way, we introduce material parameters as a sum of weighted direction-related quantities. The numerical implementation of the resulting set of constitutive is used to identify material parameters based on experimental data, exhibiting strain-induced anisotropy. In the finite-element examples, we simulate the cold-forming of amorphous thermoplastic films below the glass transition temperature subjected to different re-loading directions.