Multiscale analysis and inverse design of uncertain meso-structures (Meso-AID)

由于加工技术的重大飞跃，复杂结构的细观结构的产生已经以快速的速度发展。然而，由这样的过程产生的结构受到多方面的变化：首先，处理条件引起的微观结构中的一些散射，这反过来又导致不同的本构行为。第二，几何形状受到随机变化的影响。这些可以表现为，例如，在可变的支柱直径、连接形态的变化、局部波纹度或随机孔隙度中，仅举几例。我们承认，这些不确定性不能完全排除。因此，需要更好地了解它们对有效结构响应的影响。为了建立这一基础，我们首先针对三个主要支柱，稍后将被合并：我们建模这样的随机介观结构，并使用合理的描述符的内在随机性来表征它们。同时，我们开发直接数值模拟的基础上，最近的傅立叶加速节点求解器，将提供数据的强大的降阶模型（ROM）。ROM接受材料特性的适度变化，而不会明显损失精度。这使得它们成为生成高质量数据的理想候选者，用于进一步提供数据饥渴的方案，如深度材料网络，这些方案不需要太多但非常昂贵的预先计算。后者将被调整，使他们不仅接受可变的本构参数，但在先前建模的，随机的细观结构的几何形状的插值为目标。接下来，我们将综合这三个模块的方法，以运行正向模拟，以分析结构的随机响应及其与细观结构特征的相关性。最后，我们设想了一个直接的逆模型，建议不确定的几何形状和不确定的本构参数的组合。从而，在设计过程中的本构随机性和不确定的几何形状的平衡将是方便的：它是值得提高几何精度？是否应该追求更均匀的材料特性？哪些几何特征是关键的？

The generation of complex architectured meso-structures has developed at a rapid pace due to major leaps in processing technology. However, the structures generated by such processes are subject to manifold variations: First, the processing conditions induce some scatter in the microstructure which, in turn, results in varying constitutive behavior. Second, the geometry is subject to stochastic variations. These can manifest, e.g., in variable strut diameters, variations in junction morphology, local waviness or random porosities, to name just a few. It is accepted that these uncertainties cannot be ruled out entirely. Therefore, a better understanding of their impact on the effective structural response is required. In order to build the foundations for this, we first target three main pillars that will later be merged: We model such stochastic meso-structures and characterize them using reasonable descriptors of the intrinsic stochasticity. In parallel we develop direct numerical simulations based on recent Fourier-Accelerated Nodal Solvers that will provide data for robust reduced order models (ROMs). The ROMs accept moderate variations of the material properties without pronounced loss in accuracy. This renders them an ideal candidate for the generation of quality data for feeding further data-hungry schemes such as Deep Material Networks, which require not too many but very expensive pre-calculations. The latter will be tuned such that they not only accept variable constitutive parameters, but the interpolation across the previously modeled, stochastic meso-structural geometries is targeted. Next, we will synthesize the methods from these three building blocks in order to run forward simulations in order to analyze the stochastic response of the structures and its correlation to meso-structural features. Finally, we envision a direct inverse model which recommends combinations of uncertain geometry and uncertain constitutive parameters. Thereby, the balancing of constitutive randomness and uncertain geometry in the design process will be facilitated: Is it worth to improve geometric accuracy? Should more homogeneous material properties be pursued? Which geometric features are criticial?