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R.W. Tomas, M. Todt, T. Koch, H. E. Pettermann:
"Numerical prediction of the homogenized orthotropic linear viscoelastic material properties of composite plies and laminated composites";
Talk: 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Vienna; 2019-02-18 - 2019-02-22.

Laminated composite components made of fiber reinforced plastics show a direction dependent creep and relaxation response as a consequence of the viscoelastic matrix material. Considering direction dependent viscoelasticity in finite element simulations on the component level requires a suitable constitutive law such as the one developed in [1]. This orthotropic linear thermoviscoelastic material law is formulated under plane stress assumption making it especially suitable for shell based models mainly used in the simulation of composite structures.
The input to the constitutive model [1] in form of homogenized material data might be determined from experiments. However, the viscoelastic response of laminates depends not only on the material properties of the matrix and the fibers but also on the fiber volume fraction, the fiber orientation of the plies, and the layup. Consequently, the parameters have to be evaluated individually for each laminate making experimental procedures time consuming and inefficient. Herein, a homogenization procedure is proposed allowing to determine the required input parameters from a periodic unit cell approach reducing the experimental effort significantly. The only input data are the elastic properties of the fibers and the linear viscoelastic properties of the matrix. In a first homogenization step the effective plane stress properties of UD plies are computed using a generic periodic unit cell. With the so obtained material data the constitutive law [1] can readily be used together with layered shell elements to model composite components. Alternatively, the layered shell model can be utilized to obtain the effective properties of the laminate in a second homogenization step. The latter is beneficial when large composite components have to be simulated and ply failure can be excluded.
The procedure is exemplified for laminates consisting of glass fiber reinforced polyester resin for which the matrix data is determined from dynamic mechanical analysis (DMA) tests and the fiber data is taken from literature. The linear viscoelastic properties of UD plies, random fiber plies, and laminates with different layups are predicted and the outcomes are compared with corresponding DMA experiments.

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.

[1] H.E. Pettermann and A. DeSimone. An anisotropic linear thermo-viscoelastic constitutive law. Mech Time-Depend Mater (2017). https://doi.org/10.1007/s11043-017-9364-x