FiberMath – Realistic Microstructures for Fiber-Reinforced Composites

Efficient Material Characterization Through Virtual Testing: »FiberMath« Generates Realistic Microstructures of Fiber-Reinforced Plastics

Our software tool »FiberMath« enables the generation of realistic microstructures, which serve as the basis for the virtual material characterization of fiber-reinforced composites. Virtual characterization is an efficient and cost-effective alternative to traditional physical testing. The structures generated by »FiberMath« precisely and reliably model the geometry of fiber-reinforced composites.

The experimental characterization of fibre-reinforced composites is complex and expensive. This is due to their high local variability (differences in structure at different points) and anisotropy (properties that vary depending on the direction, such as strength or stiffness). Virtual tests offer an efficient alternative: they supplement physical measurements with computer-aided tests on virtually generated microstructures.

 

Why Virtual Tests?

In order for virtual tests and material optimization methods to be meaningful, realistic geometries on the micrometre scale must be available. The variety of fiber geometries – which differ in terms of fiber orientation, length distribution, curvature and volume content – poses a major challenge. Although digital images, e.g. from microcomputed tomography, offer detailed insights, they cannot cover the entire parameter range of possible fiber geometries. This is where synthetic digital twins come into play to close this gap.

Create Virtual Structures With FiberMath

With our »FiberMath« tool developed at the Fraunhofer ITWM, realistic microstructures of fiber-reinforced composites can be created. The tool is particularly suitable for materials with high fiber volume fractions and effectively prevents fiber overlap. In combination with »FeelMath«, »FiberMath« enables a fast and precise calculation of the mechanical properties depending on the fiber geometry. The generated geometry meets the requirements with high accuracy and reliability.

Mit FiberMath erzeugte Mikrostruktur mit geraden Fasern
© Fraunhofer ITWM
Mit FiberMath erzeugte Mikrostruktur mit geraden Fasern
Mit FiberMath erzeugte Mikrostruktur mit gekrümmten Fasern
© Fraunhofer ITWM
Mit FiberMath erzeugte Mikrostruktur mit gekrümmten Fasern
Mit FeelMath berechneter richtungsabhängiger E-Modul für beide Strukturen
© Fraunhofer ITWM
Mit FeelMath berechneter richtungsabhängiger E-Modul für beide Strukturen

Flexibility for Complex Structures

»FiberMath« offers comprehensive configuration options for microstructures:

  • Multiple Fiber Types: Each type has its own geometry parameters and can be mixed or arranged in layers.
  • Typical Applications: Simulations of structures with planar-isotropically oriented middle layers, as they occur in injection-molded components.
  • Particles: besides fibers, also structures with spherical particles can be generated.

Adjustable Parameters per Fiber Type:

  • Fiber Length Distribution: Fitting of a combined Weibull-Lognormal distribution to an empirically determined fiber length distribution or constant fiber length
  • Fiber Diameter
  • Fiber Orientation: From isotropic to planar-isotropic to unidirectional
  • Fiber Volume Fraction: Reliable generation of structures with high fiber volume ratios
  • Maximum Fiber Curvature: Generation of structures with straight or curved fibers