Numerical Analysis of material uncertainties in components with microheterogeneous ranges

• Applicant: Dr. Carla Beckmann
• Subject Area: Mechanical Properties of Metallic Materials and their Microstructural Origins
• Term: from 2016 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 317072826

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.

• DFG Programme: Research Grants