Formulation and implementation of a constitutive model for semicrystalline polymers

• The mechanical behaviour of semicrystalline polymers has been successfully modelled.
• Novel constitutive formulations at the microscopic material level have been introduced.
• A new homogenization method to bridge the scales of the material has been proposed.
• The model has been validated by comparison with experimental data.
• The applicability of the model is shown for different structural investigations.

The paper outlines a new constitutive model and its numerical implementation for the mechanical behaviour of semicrystalline polymers. Essential for the constitutive model is a homogenization approach that makes use of a representative mesostructure (RMS) and of the micromechanical description of the two characteristic phases of semicrystalline polymers, the amorphous and the crystalline phase. A homogenization approach is used to characterise the macroscopic element by extracting the macroscale characteristics of the material from the results of a microscale boundary value problem. For the microscopic amorphous constitutive model, a new evolution law is introduced for the athermal shear stress to the constitutive model proposed by Miehe et al. (2009), who developed a constitutive formulation for amorphous polymers in the logarithmic strain space. For the microscopic crystalline model, the approach proposed by Simo (1988a), who numerically implemented an algorithm for plasticity for crystalline materials, is transformed into a logarithmic kinematical framework. The modelling capability of the proposed formulation is verified by comparison of numerical simulations to experimental investigations carried out by the Leibniz-Institut für Polymerforschung (IPF) Dresden. The experiments were performed on isotactic polypropylene (iPP) and the mechanical tensile and compression tests were carried out at different temperatures. The model is also used for quasi-static (QS) and dynamic (DY) simulations of an iPP car bumper.