A multi-level finite element method for modeling rubber-toughened amorphous polymers

Polymers are intrinsically tough although they can suffer fromextreme localization of the deformation. A pronounced softeningafter yield, followed by a low hardening, promotes this extremelocalization. Post-yield behavior is directly related to the polymerentanglement density, thus to the chain stiffness. A number of -rather academic- experiments, using (in order of increasingentanglement density) Polystyrene (PS), Polymethylmetacrylate(PMMA) and Polycarbonate (PC), clearly demonstrate theimportance of the intrinsic post-yield behavior on the macroscopicresponse. Furthermore polymers differ in their capability ofsustaining triaxial stresses, yielding cavitation and -ultimatelycrazing.This phenomenon causes notch sensitivity of all polymers,including the so-called tough PC. To overcome thi! s problem, thematerials should be made heterogeneous. This paper addresses theuse of the Multi-Level Finite Element Method to analyze theheterogeneous deformation of two-phase polymer blends. Twoimportant length scales are considered: the heterogeneous RVE(representative volume element) and that of the continuous scale.Analyses like these not only improve our understanding of thephenomena that occur on the different scales, but also givedirections towards improvement of existing materials.