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.

在本文中，提出了一种用于复合材料设计的多尺度优化方法。目标是为短纤维增强聚合物 (SFRP) 寻找不同的材料设计，使其具有所需的有效（通常各向异性）粘弹性行为。该论文扩展了 Staub 等人的工作。(2012) 并提出了材料均质化、代理建模、参数优化和稳健性分析的组合。考虑了各种微观结构设计参数，包括纤维体积分数、纤维取向分布、线性弹性纤维特性和温度相关材料行为。为了解决结构优化问题，开发了一个基于代理的优化框架。该框架的各个步骤包括使用实验设计 (DoE) 对约束材料设计空间进行采样，使用数值均匀化创建材料特性数据库，使用替代建模方法插值单个有效粘弹性参数，以及使用差分进化 (DE) 进行优化。在数值均匀化步骤中，对虚拟创建的代表性体积元素 (RVE) 进行蠕变模拟，并使用基于快速傅里叶变换 (FFT) 的均匀化来获得有效的粘弹性材料参数。对于每个确定的优化设计，都会评估稳健性。所考虑的 Kriging 类型的 Kriging 代理模型具有很高的预测精度。数值示例证明了所提出方法在确定具有目标粘弹性行为的 SFRP 方面的效率。实验验证表明均匀化方法与相应的测量结果非常吻合。在复合材料部件的制造过程中，此类优化的结果允许考虑局部微观结构，以实现所需的宏观粘弹性行为。