Modeling, Simulation, and Optimization of the Mechanics of Woven Structures

3D Gewebe Biegung

3D fabric bending

The aim of this joint DFG project with the department of Applied Mechanics at FAU Erlangen is to create simulations to optimize the structure of:  

  • woven or knitted fabrics
  • 3D knitwear
  • fiber materials with heterogeneous microstructures

A special focus will be given on the contacts between individual threads or fibers. The consideration of contact leads to a non-linear problem and the different geometric length scales make direct numerical simulation extremely complex. This is why a multi-scale approach has been chosen to facilitate dimension reduction of the problem.


The Problem has Two Small Parameters:

  • the relationship between periodic or representative patterns in the fabrics and the overall fabric dimensions
  • the relationship between fiber (or yarn) diameter and its length

Mathematically asymptotic methods are named homogenization or dimension reduction relative to the first or second small parameter. In homogenization, the aim is a scale separation on the basis of auxiliary problems using a periodicity or representative structural unit cell to facilitate the derivation of the overall effective material behavior of the fabric.

A dimension reduction (asymptotic in terms of the fiber thickness) reduces the fabric to a beam network, where the total displacement can be computed as a superposition of the stretch, bending, and torsion of one-dimensional beams. The mechanical contact between the beams must be explicitly taken into account.

Optimierung der Gestrickgeometrie

Optimization of the gesture geometry with respect to the cross-contraction number

Design of New Textiles Possible

The computational algorithms corresponding to the contact problem are implemented using a beam Finite Element Method expanded with beam elements. In addition, besides the calculation of the effective mechanical material properties for various existing woven and knitted fabrics for industrial and medical applications, the approach also has the potential in the targeted design of new fabrics with predefined mechanical property profiles.

For example, the goal may be to achieve a certain stress profile while optimizing the local fabric structure for a deformed woven or knitted fabric. In a two-step iterative process based on the initial fabric design, the effective macroscopic stress distribution is calculated and compared to the desired profile, and the differences are minimized by a gradient algorithm.

The result is a set of parameters that describe the optimal fabric structure for the intended purpose. Additionally, various finishes can be simulated and analyzed for the fabric finishing processes. This allows the quality of the resulting fabric finish to be assessed in advance and, ultimately, prevents the formation of wrinkles and other optical inhomogeneities.


Pulling on a textile

Aufziehen eines Textils

Pulling on a textile