Multiscale optimization of the viscoelastic behavior of short fiber reinforced composites

In this paper, a multiscale optimization approach for composite material design is presented. The objective is to find different material designs for a short fiber reinforced polymer (SFRP) with a desired effective (in general anisotropic) viscoelastic behavior. The paper extends the work of Staub et al. (2012) and proposes a combination of material homogenization, surrogate modeling, parameter optimization and robustness analysis. A variety of microstructure design parameters including the fiber volume fraction, the fiber orientation distribution, the linear elastic fiber properties, and the temperature dependent material behavior are considered. For the solution of the structural optimization problem, a surrogate-based optimization framework is developed. The individual steps of that framework consist of using design of experiments (DoE) for the sampling of the constraint material design space, numerical homogenization for the creation of a material property database, a surrogate modeling approach for the interpolation of the single effective viscoelastic parameters and the use of differential evolution (DE) for optimization. In the numerical homogenization step, creep simulations on virtually created representative volume elements (RVEs) are performed and a fast Fourier transform (FFT)-based homogenization is used to obtain the effective viscoelastic material parameters. For every identified optimal design, the robustness is evaluated. The considered Kriging surrogate models of Kriging type have a high prediction accuracy. Numerical examples demonstrate the efficiency of the proposed approach in determining SFRPs with target viscoelastic behavior. An experimental validation shows a good agreement of the homogenization method with corresponding measurements. During the manufacturing of composite parts, the results of such optimizations allow a consideration of the local microstructure in order to achieve the desired macroscopic viscoelastic behavior.