Texmath Software Tool for the Simulation of Knitted, Woven and Warp Knitted Fabrics

Knitted and woven fabrics are produced with the aid of knitting or weaving machines. Each textile is based on a looping diagramm, which is read into the machine or is firmly pre-defined in the machine. MeshUp is the software module of TexMath, in which looping diagramm for various woven and knitted fabrics with different types of binding, the yarn path and all contact points between different yarns are created, graphically displayed and translated into the corresponding input formats for further simulations in TexMath with FISFT and FiberFEM. In addition, MeshUp also provides the geometry as volume data (voxel format) for calculation tools such as GeoDict and FeelMath.

With FiberFEM, woven and braided textiles, spacer fabrics, scrims and trusses can be calculated and optimized regarding their effective mechanical material properties. A special feature of FiberFEM is that, in addition to tensile and shear properties, effective bending and torsional properties of textiles can also be determined based on their textile structure and yarn properties.

As input variables FiberFEM requires the microstructure description from MeshUp, the fiber cross-section geometry, as well as mechanical fiber properties such as tensile stiffness and friction. As output the effective mechanical textile quantities are calculated. Besides the calculation of the effective mechanical material properties for already existing woven or knitted textiles for technical and medical applications, the approach also offers the potential for the targeted design and optimization of new textiles with a given mechanical property profile.

For example, the relaxation behavior of a textile can be determined from the weave or knit pattern and the yarn relaxation times for viscoelastic yarns. Coefficients of friction between the yarns are also taken into account and are directly included in the simulation of the effective properties or identified from the experimental validation with the fabric.

The tool FIFST is specialized for dynamic simulations of stretchable knitted fabrics and teir production. For example, the knitting process can be simulated, the pull-off from the knitting machine, the shrinkage to a relaxed textile and also the further deformation during tightening can be calculated. This means that the design of the knitted fabric can also be adapted to predefined tension profiles and individualized machine control is possible for the production of personalized textiles or product-specific designs.

The numerical implementation uses the finite element method with non-linear truss elements, which has been extended for contact problems by an additional internal variable - the sliding of threads at contact nodes. The friction law is implemented with the Euler-Eutelwein model, which was extended by an additional adhesion term. Adhesion thus allows different pre-strains in the respective meshes. The elastic energy is calculated directly from the yarn force-elongation curves. 

One of the most important unique selling points of FIFST is the special technology of assigning several elements to specific threads and their arrangement in the thread as well as the simultaneous contact sliding at millions of nodes. Thus FIFST enables multi-scale simulation of large knitted or woven shell components, taking into account the local textile structure.