TexMath Software Tool Simulates Knitted and Woven Fabrics

TexMath is a modular software program which enables simulations of multi-scale problems of solid mechanics for specific textile applications. Tools are based on algorithms for dimension reduction and homogenization. 

Periodic textile structures with complex bonds can be created with the structure generator (MeshUp). Another component called FiberFEM then computes the effective mechanical properties of recurring structures under infinitesimal strains. Alternatively, the FISFT component can be used for long stretching and is ideal for simulations of complex load scenarios on textiles or even while in production, such as knitting.

Each of these tools interfaces with the others as well as with GeoDict, if required for additional simulations of fluid mechanics, for example, to compute the fabric’s permeability in each stretched state. By means of the interface with FeelMath, the possibility of a detailed, three-dimensional mechanical simulation of individual yarns is presented, which allows the strength and durability of specific yarns to be examined at their contact nodes within the fabric.


MeshUp Component Generates Woven and Knitted Structures

3D Gewebe Zug
3D Textile Pattern

Knitted and woven fabrics are produced using knitting and weaving machines. Each fabric has a basic interloop or weave, which is defined in advance and entered in the machine parameters to produce a special textile product.

MeshUp is one of the TexMath software components and is used to generate textile patterns with all the details of the interlooping, contact, connectivity and cross-sections of cylindrical curves (yarns). It creates a graphic visualization and translates finite element-structures with the corresponding thread label for the subsequent TexMath, FISFT and FiberFEM simulations into corresponding input formats. Moreover, MeshUp prepares the geometry in volume data format (voxel format) for simulation with the GeoDict and FeelMath tools.

FiberFEM to Compute the Effective Mechanical Properties of a Periodic Structure with Beam Element Contacts

Kompression Abstandsgewirke
Compression of Spacer Weaves
Structure in the FiberFEM Model

FiberFEM is a tool for calculating and optimizing the mechanical material parameters of:

  • woven and laced textiles,
  • spacer weaves,
  • frames, 
  • and fiber structures.

In addition to the tension and shear properties, a special feature of FiberFEM is the ability to simulate effective bending and torsion properties of textiles or spacer weaves on the basis of their textile structure and the properties of the yarns or fibers.

Furthermore, the relaxation times can be determined from the web cartridge or structural designs for viscoelastic fiberse. Even the coefficient of friction between the fibers is taken into account and can be included directly in the simulation of the effective properties or identified from the experimental validation with the fabric. FiberFEM has both numeric and symbolic solvers, which enables the optimization of the textile structure or the specific binding cartridge for the required textile properties.

As the input variables, besides the description of the micro-structure or via a connecting cartridge of the textile, FiberFEM requires the fiber cross section geometry and the mechanical parameters, like tensile stiffness and friction. The effective mechanical textile ratios are returned as output. In addition to the calculation of the effective mechanical textile properties for a large number of already existing woven and knitted textiles used in technical and medical applications, the approach also offers the potential for the design of new textiles with a defined mechanical properties profile.

Abzug aus der Strickmaschine.
Removal from the Knitting Machine
Abzug aus der Strickmaschine
Removal from the Knitting Machine

The FISFT model is specially design for the dynamic simulation of knitted fabrics, very elastic weaves, and knitwear. It can simulate the knitting process as well as compute the removal from the knitting machine, the shrinkage of the "relaxed" textile, and even the internal forces when putting it on. The design can be adjusted to a predefined stress profile and a customized machine control over the production of individual textiles or product-specific designs is possible.

For the numeric implementation, the Finite-Element-Method with non-linear truss elements is used as the tool, which is expanded by an additional internal variable for the contact problem – sliding of the threads over the contact nodes. The friction law is implemented with the Euler-Eutelwein model for elastic ropes, which has also been expanded in the model with an additional adhesion term.

The adhesion enables different pre-stressing in the respective stitching. The elastic energy is computed directly from the fiber force expansion curves. The resulting non-linear problems are solved for elastic deformation and slippage under the frictional force in two separate Newtonian processes. The crossing angle between the threads in each deformation step is adapted to the current configuration.

A key unique feature of FISFT is the special technology for associating multiple element to specific threads and their arrangement on the thread and at the same time the sliding contact to a million knot points. In this way, FISFT enables multi-scale simulation of measures of knitted and woven shell components while accounting for the local textile structure.