Numerical Analysis of material uncertainties in components with microheterogeneous ranges

目前的建议的目的是开发一种方法的数值有效的确定和建模的材料不确定性的轻质结构组成的随机微观非均质材料，如固体泡沫。这种方法是必需的设计结构和组件，因为经典的确定性概念是不适当的统计微观非均匀体。为此，应采用具有闭孔泡沫芯的夹层结构为例，开发概率方法。这种方法将允许确定有效的材料特性和相应的分散的微观结构特性的基础上的分散。必要的输入参数，如细胞尺寸，形状和取向的细胞微观结构和相应的概率分布可以通过计算机断层扫描。特别是，应开发一种方法，解释微观结构各向异性对有效材料性能的影响。为了开发基于微观结构模拟的概率本构关系，需要实现一种用于生成具有伸长拉伸和拉伸取向单元的有限元模型的算法。为此目的，将定义一个修改的Voronoprene过程在Laguerre几何。由于基于其真实的微观结构的大型部件的直接建模是极其广泛的且不可行的，因此微观结构有限元分析仅用于概率本构律的定义。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。该模型将验证对实验研究的试样和半结构水平，使用4点弯曲实验。要开发的模型的主要优点-相比，经典的确定性分析-是它的可靠性和数值相当有效的预测的不确定性在大型组件的结构响应的能力，因为在微观力学水平上的概率模拟只需要的概率本构关系的定义。因此，一种计算方法将是可用的，这是能够预测的不确定性，预计在大型结构的基础上的随机材料特性。

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.