Numerical Analysis of material uncertainties in components with microheterogeneous ranges

当前提议的目标是开发一种方法，用于对部分由随机微非均质材料组成的轻型结构中的材料不确定性进行有效的数值确定和建模，例如固体泡沫。这种方法在结构和部件的设计中是必需的，因为经典的确定性概念不适用于统计上的微异质物体。为此，应开发一种概率方法，使用带有闭孔泡沫芯的夹层结构的例子。这种方法将允许在分散的微观结构性质的基础上确定有效的材料性质和相应的散射。通过计算机层析成像可以获得所需的输入参数，如细胞大小、形状和细胞微结构的取向以及相应的概率分布。特别是，应开发一种方法，考虑微结构各向异性对有效材料性能的影响。为了发展基于微观结构模拟的概率本构关系，需要实现一种生成具有拉长、拉伸和可变取向单元的有限元模型的算法。为此，将在Laguerre几何中定义一个改进的Voronoí过程。由于基于真实微观结构的大型构件直接建模是非常广泛和不可行的，微观结构有限元分析只能用于定义概率本构关系。在其使用中，输入参数是最基本属性的分布、属性之间的相关性以及它们的空间相关性。该模型将通过四点弯曲实验在试件水平和半结构水平上进行验证。与经典的确定性分析相比，将要开发的模型的主要优点是它能够可靠和数值地相当有效地预测大型部件结构响应的不确定性，因为只需要在微观机械水平上进行概率模拟来定义概率本构关系。因此，将有一种计算方法能够基于随机材料特性来预测大型结构中预期的不确定性。

The objective of the current proposal is the development of a method for the numerically efficient determination and modelling of material uncertainties in lightweight structures consisting partially of stochastic microheterogeneous materials, e.g. solid foams. Such methods are required in the design structures and components, since classical deterministic concepts are inappropriate for statistically microheterogeneous bodies. For this reason, a probabilistic method shall be developed, using the example of a sandwich construction with a closed-cell foam core. This method will allow the determination of the effective material properties and the corresponding scatter on the base of the dispersed microstructural properties. The necessary input parameters such as cell size, shape and orientation of the cellular microstructure and the corresponding probability distributions can be obtained by computed tomography. In particular, a method shall be developed, accounting for the effect of microstructural anisotropy on the effective material properties. For the development of the probabilistic constitutive law based on microstructural simulations, an algorithm for generation of finite element models with elongated stretched and variably orientated cells needs to be implemented. For this purpose, a modified Voronoï process in Laguerre geometry will be defined. For the reason that direct modeling of large-scale components based on their real microstructure is extremely extensive and not feasible, the microstructural finite element analysis shall only be used for definition of a probabilistic constitutive law. In its use, the input parameters are the distributions of the most essential properties, the correlation between the properties as well as their spatial correlation. The model will be validated against experimental investigations on coupon and semi-structural level using 4-point-bending experiments. The main advantage of the model to be developed - compared to classical deterministic analyses - is its ability for the reliable and numerically rather efficient prediction of the uncertainty in the structural response of large-scale components since the probabilistic simulations on the micromechanical level are required only for the definition of the probabilistic constitutive law. Thus, a computational method will be available which is able to predict the uncertainties to be expected in large-scale structures based on a stochastic material characterization.