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T. Ceglar, H. E. Pettermann:
"Finite element simulations and nonlinear homogenization of fibre reinforced elastomer composite";
Vortrag: 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Vienna; 18.02.2019 - 22.02.2019.

Fibre reinforced elastomers (FREs) made of continuous fibres embedded in a hyperelastic matrix exhibit highly anisotropic properties. The fibres provide excellent stiffness and strength in the fibre direction while the matrix allows considerable deformations and large failure strain perpendicular to the fibres. Such materials are widely used in tyres, power transmission belts and are also present in biological tissues.
The pronounced anisotropic nature of FREs and the strong influence of shape, size and arrangement of fibres make it difficult to successfully employ analytical homogenization strategies. Most of the available anisotropic hyperelastic material models for the homogenized behaviour are purely phenomenological and are typically subject to non-trivial material parameter fitting. However, they are essential for structural analysis of components made from FREs.
In the present work, the effective response of aligned continuous glass fibres randomly embedded in a silicon rubber matrix is predicted for selected load cases by means of nonlinear Finite Element Method (FEM) unit cell simulations. The effective response is studied in the finite strain regime with respect to different fibre arrangements and sizes of unit cells.
Besides the nonlinear homogenization by the unit cell simulations, phenomenological anisotropic hyperelastic material models are employed to approximate the effective behaviour of FREs. Most of their material parameters can be calibrated by consideration of the linearised initial behaviour. For the anisotropic hyperelastic material models considered in this work, the fitting is minimised to adjust a single parameter, which influences the nonlinear progression in the response.
Unit cells with periodic boundary conditions are simulated in transverse, axial and combined load cases. The effective response of unit cells under each load case are compared to the single element simulations utilizing the calibrated phenomenological material models. Good agreement between the results is found for moderate stretches and fibre volume fractions of 20%-30%.

Acknowledgement:
The funding of the Polymer Competence Center Leoben GmbH (PCCL) within the COMETprogram by the Austrian Federal Ministry for Transport, Innovation and Technology (BMVIT), the Austrian Federal Ministry of Digital and Economic Affairs (BMDW), Österreichische Forschungsförderungsgesellschaft mbH (FFG), the Provinces of Styria, Lower Austria and Upper Austria is gratefully acknowledged.