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

TL;DR

This paper presents a new greedy algorithm for efficiently simulating 3D nonwoven fabrics by estimating fiber direction distributions, significantly reducing computation time compared to traditional methods.

Contribution

A novel greedy algorithm for sparse estimation of fiber direction PDFs that accelerates 3D fabric simulation significantly.

Findings

Reduction of computation time from 40 days to 41 minutes for 100 fibers

Effective simulation of fiber directions based on real CT scan data

Demonstration of the algorithm's efficiency on synthetic and real examples

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.