Multi-scale constitutive modeling of the small deformations of semi-crystalline polymers

A multi-scale constitutive model for the small deformations of semi-crystalline polymers such as high density Polyethylene is presented. Each macroscopic material point is supposed to be the center of a representative volume element which is an aggregate of randomly oriented composite inclusions. Each inclusion consists of a stack of parallel crystalline lamellae with their adjacent amorphous layers.Micro-mechanically based constitutive equations are developed for each phase. A viscoplastic model is used for the crystalline lamellae. A new nonlinear viscoelastic model for the amorphous phase behavior is proposed. The model takes into account the fact that the presence of crystallites confines the amorphous phase in extremely thin layers where the concentration of chain entanglements is very high. This gives rise to a stress contribution due to elastic distortion of the chains. It is shown that the introduction of chains’ elastic distortion can explain the viscoelastic behavior of crystalline polymers. The stress contribution from elastic stretching of the tie molecules linking the neighboring lamellae is also taken into account.Next, a constitutive model for a single inclusion considered as a laminated composite is proposed. The macroscopic stress-strain behavior for the whole RVE is found via a Sachs homogenization scheme (uniform stress throughout the material is assumed).Computational algorithms are developed based on fully implicit time-discretization schemes.