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Three-dimensional simulation of nonwoven fabrics using a greedy approximation of the distribution of fiber directions

: Gramsch, S.; Kontak, M.; Michel, V.


Zeitschrift für angewandte Mathematik und Mechanik : ZAMM 98 (2018), Nr.2, S.277-288
ISSN: 0044-2267
ISSN: 0946-8463
ISSN: 1521-4001
Fraunhofer ITWM ()

An elementary algorithm is used to simulate the industrial production of a fiber of a 3-dimensional nonwoven fabric. The algorithm simulates the fiber as a polyline where the direction of each segment is stochastically drawn based on a given probability density function (PDF) on the unit sphere. This PDF is obtained from data of directions of fiber fragments which originate from computer tomography scans of a real nonwoven fabric. However, the simulation algorithm requires numerous evaluations of the PDF. Since the established technique of a kernel density estimator leads to very high computational costs, a novel greedy algorithm for estimating a sparse representation of the PDF is introduced. Numerical tests for a synthetic and a real example are presented. In a realistic scenario, the introduced sparsity ansatz leads to a reduction of the computation time for 100 fibers from around 80 days to 2.5 hours.