Keywords: computational homogenization, multi-scale material modeling, semicrystalline polymers, isotactic polypropylene..

The computational homogenization scheme, presented in this paper, provides an efficient and precise framework for bridging the scales within heterogeneous materials and structures with large length scale differences. The approach is generally applicable to investigations at large deformations and material inelasticity. The novel kinematical basis is the generally non-zero length scale difference of the scales under observation which implies a coupling of the scales. Consequently, the displacement fields of the different scales interact with and influence each other in e.g. a mechanical loading scenario. The contribution to homogenization methods determines any equilibrium state of the investigated macrostructure directly by the equilibrium of the embedded microscale. The improved efficiency and reliability of the approach presented is demonstrated by a comparison with existing computational homogenization schemes. Furthermore, an application of the novel multi-scale approach is presented by describing the constitutive mechanical behavior of semicrystalline polymers. The modeling capability of the proposed constitutive formulations combined with the homogenization scheme is verified by a comparison of numerical simulations to experimental investigations carried out by the Leibniz Institute of Polymer Research Dresden (IPF). The experiments are performed on isotactic polypropylene (iPP) at different temperatures. The validation demonstrates a successful prediction of the mechanical behavior of semicrystalline polymers.

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