Prediction of the uncertainty in the response of foam core sandwich structures due to disordered microstructure of the material

Solid foams are important core materials in sandwich construction since they combine a rather low specific weight with a reasonable stiffness and strength. Further benefits derive from their inherent good thermal and acoustic damping characteristics. Compared to other materials such as honeycomb structures, solid foams have the advantage that they can easily be processed to any desired shape. On the other hand, disadvantages derive from their disordered microstructure leading to uncertainties in their macroscopic material response. The present study deals with a numerical scheme for prediction of the uncertainties in the effective material response, based on the known geometric uncertainty of the microstructure. For this purpose, a probabilistic homogenization scheme is proposed. In contrast to deterministic approaches, where the average stress-strain behavior of statistically representative volume elements is analyzed, small scale, "testing volume elements" are considered, since - especially for foams with large cell sizes - a statistically representative volume element might have edge lengths in the same order of magnitude as the smallest characteristic length of the sandwich structure, e.g. the core thickness. As the smallest feasible testing volume elements, the individual cells of a large-scale foam model generated randomly by means of a Voronoï process in Laguerre geometry are considered. The results of the testing volume element analyses are evaluated by stochastic methods, considering the probability distributions of the effective properties as well as the correlation between the properties at neighboring points of the effective material. In a case study, a single edge clamped sandwich beam with a foam core is considered. The core material is modeled as a random field with properties determined in the aforementioned probabilistic homogenization analysis. Whereas the material uncertainty is found to cause only minor scatter in the deformation of the beam, significant uncertainties are observed in the strength of the considered structure.