Generating Realistic Microstructures of Fiber-reinforced Composites
GeoApp: FiberMath
The experimental characterization of the mechanical behavior of fiber-reinforced composites is often difficult, due to their inherent local variability and anisotropy. Digital testing helps in reducing this effort by complementing a limited number of measurements with simulations on digitally generated geometries.
Digital testing, as well as digital material optimization methods, rely on an accurate representation of the geometry at micrometer scale. The geometry of fibers varies in terms of fiber types, orientations, length, curvature, and volume content. While digital images at this scale are often accessible through methods like micro-CT, they cannot cover the whole parameter range of possible fiber geometries. The FiberMath GeoApp plays an indispensable role in supplementing these imaging techniques by providing synthetic digital twins.
Generation of digital microstructures
The FiberMath GeoApp generates realistic microstructures of fiber-reinforced composites with high volume fractions and without fiber overlap. Pairing the ElastoDict module with the FiberMath GeoApp lets you quickly and easily work out how the composite material will behave mechanically, depending on the geometry of the fibers.
FiberMath generates structures with several fiber types, each with their own set of geometry parameters. Fiber types can either be mixed or separated into layers in the depth direction. This allows, e.g., the generation of structures with a middle layer where the fiber orientation is planar-isotropic, as it is typical for injection-molded components.
The following fiber parameters need to be specified for each fiber type:
- Fiber length
- Fiber diameter
- Fiber orientation: All possible fiber orientation tensors, from isotropic to planar-isotropic and unidirectional.
- Fiber volume fraction: FiberMath can generate structures with high volume fractions, such as those used in many industrial applications.
- Maximal fiber curvature: FiberMath can generate straight and curved fibers.
Digital generation of fiber-reinforced microstructures
- Precise description of fiber geometry
- Fiber length
- Fiber diameter
- Fiber orientation
- Fiber volume content
- Fiber curvature
- Combination of different fiber types
- As mixture
- As a layered structure
Comparison of microstructures with
straight and curved fibers
(a) Generated microstructure with straight fibers
(b) Generated microstructure with curved fibers
Influence of curvature on
effective stiffness
Generation setup
The FiberMath GeoApp guides the user through the input process for the generation of digital fiber structures. The input includes numerical parameters, such as the mesh size, which enables the generation of structures comprising multiple fiber types, either combined or separated into distinct layers in the depth direction..
Summary of features
- Fiber geometry: Define the mean orientation, volume content, length, curvature, and diameter for each type of fiber in the geometry.
- Mesh settings: Set the resolution and the number of voxels of the resulting geometry.
- Output: Choose the formats in which the output is written.
With the FiberMath GeoApp, the user generates realistic digital microstructures of fiber-reinforced materials over a wide parameter range. FiberMath offers an accurate geometric representation of fiber structures at the micro scale, thereby enabling the digital evaluation of an extensive array of potential material designs and the execution of digital tests on composite materials.
Following modules are often used with the FiberMath GeoApp:
| Import & Image Processing | ImportGeo-Vol |
| Image Analysis | MatDict |
| Material Modeling | FiberGeo |
| Simulation & Prediction | ElastoDict |