Multiscale modeling of continuous fiber and fabric reinforced rubber components

Fabric or continuous fiber reinforced rubber components (e.g. tires, air springs, industrial hoses, conveyor belts or membranes) are underlying high deformations in application and show a complex, nonlinear material behavior. A particular challenge depicts the simulation of these composites. In this contribution we show the identification of the stress and strain distributions by using an uncoupled multiscale modeling method, see [1]. Within this method, two representation levels are described: One, the meso level, where all constituents of the composite are shown in a discrete manner by a representative volume element (RVE) and secondly, the macro level, where the structural behavior of the component is defined by a smeared anisotropic hyperelastic constitutive law. Uncoupled means that the RVE does not drive the macroscopic material behavior directly as in a coupled approach, where a RVE boundary value problem has to be solved at every integration point of the macro level. Thus an uncoupled approach leads to a tremendous reduction in numerical effort because the boundary value problem of a RVE just has to be solved at a point of interest, see [1]. However, the uncoupled scale transition has to fulfill the HILL–MANDEL condition of energetic equivalence of both scales. We show the calibration of material parameters for a given constitutive model for fiber reinforced rubber by fitting experimental data on the macro level. Additionally, we demonstrate the determination of effective properties of the yarns. Finally, we compare the energies of both scales in terms of compliance with the HILL–MANDEL condition by using the example of a biaxial loaded sample and discuss the consequences for the mesoscopic level. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)