Modeling uniform random distributions of nonwoven fibers for computational analysis of composite materials.

• Bertrand's paradox for chords on a circle can be extended to fibers on a square, with many methods of fiber placement. • A combination approach of fiber placement methods can arrive at an acceptable level of uniformity. • Homogeneous fiber layout requires invariance to Euclidean transformations: rotation, scale, and translation. • Fiber "line density" and "fragment size" are defined and used to evaluate methods of uniform random fiber placement. • The proposed exact solution creates homogeneous uniform random fiber placement for the creation of digital twin geometry. This paper considers the random placement of fibers on a square to achieve a desired homogeneous uniform distribution, as required in production of digital twin geometry for computational analysis of composite materials. Six methods of random fiber placement were demonstrated. Bertrand's paradox for placement of random chords on a circle provided the framework to compare, contrast, and evaluate similar methods for placing fibers on a square. Simulations were performed with chord placement on a circle and fiber placement on a square. Results were evaluated using uniformity of areal line density and fragment size distributions. A combined approach for placement of fibers on a square was developed that achieved homogeneous uniform distribution. A proposed exact solution to achieve the desired uniform distribution was demonstrated. A statistical analysis and data regression demonstrated the homogeneous results achieved by the combined approach and the proposed exact solution. The objectives of this paper were achieved through demonstration of both a combined approach and a proposed exact solution to random fiber placement on a square to achieve homogeneous, uniform distribution of fibers for use in digital twin geometry for computational testing of composite materials. [ABSTRACT FROM AUTHOR]