Geometric and Mechanical Modeling of Fiber-Reinforced Composites

Micro-computed tomography (µCT) yields three dimensional reconstructions of the microstructures of materials down to a spatial resolution of about 1 µm. Based on the resulting image data, many mechanically relevant geometric parameters can be computed using three dimensional image analysis. These parameters include fiber density, orientation, homogeneity and thickness. We show how to fit stochastic fiber models to this image data. Such models take into account fiber densities, orientations, radii and inhomogeneities. These geometries can be realized, thus enabling numerical homogenization methods based on the Lippmann-Schwinger equations in elasticity. These yield the full elastic tensor and even nonlinear elastic behavior. With appropriate damage models, the material strength can be characterized. Such an approach has various advantages over mechanical testing. For example, it characterizes a material in every direction, instead of only the direction in which a tensile test was performed. Furthermore, material models open the path to virtual material design, where one can use computer experiments to identify the microstructural geometry which best fulfills the requirements in some given application. In this contribution, we demonstrate the entire chain consisting of image analysis, geometric and mechanical modeling for glass fiber-reinforced thermoplastics.