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arXiv · 1608.01514

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

Simone Gramsch·Max Kontak·Volker Michel
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Abstract

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 non-woven 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 nearly 40 days to 41 minutes.

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Simone Gramsch, Max Kontak, Volker Michel. 2016-08-04. Three-dimensional simulation of nonwoven fabrics using a greedy approximation of the distribution of fiber directions. https://arxiv.org/abs/1608.01514

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