GeoDict TexMath GeoApp – Digital Modeling of Knitted Textiles

TexMath GeoApp is a parametric digital microstructure generation tool developed by Math2Market for weft‑knitted, warp‑knitted, and 3D spacer fabrics. Based on actual design parameters such as knitting pattern, yarn diameter, row density, needle density, and layer spacing, it can rapidly create 3D periodic structures. It supports different yarn material combinations and user‑defined model resolutions.

1. From Knitting Parameters to 3D Microstructures

Unlike CT‑based reconstruction of existing materials, TexMath generates structures directly from design parameters. For a given knitted fabric, users can define the yarn diameter, the count of rows per unit length (row density), the count of needles per unit length (needle density), and the layer spacing for multi‑layer and 3D spacer fabrics. Different yarns can be assigned different materials, so the model is not limited to homogeneous structures but can also describe complex knitted systems containing multiple yarn materials.

2. From Flat Knitted Fabrics to 3D Spacer Fabrics

By adjusting geometric parameters, TexMath can generate a wide variety of weft‑ and warp‑knitted structures, ranging from traditional flat knitted fabrics to complex 3D spacer fabrics. The generated fabrics are periodic structures. Users can freely define the number of periodic repetitions, the final model dimensions, and the spatial resolution. The same basic knitting pattern can be used to generate either a small representative unit cell or a larger 3D digital fabric by repeating the pattern.

3. Key Geometric Design Parameters

The adjustable parameters include the fabric pattern (which determines the basic loop and yarn connections), yarn diameter (affecting pore space, solid fraction, and transport channels), rows per unit length (controlling knitting density in one direction), needles per unit length (controlling density in the other direction), layer spacing (for multi‑layer and spacer fabrics), yarn material (supporting combination of different materials), number of periodic repetitions (determining the extent of structure expansion), and spatial resolution (determining model geometric precision). All these parameters can be adjusted independently to explore a wide design space.

4. Acoustic Performance – Predicting Sound Absorption from Microstructure

Fabrics are widely used for noise reduction in automotive and other industrial environments. Once TexMath generates the fabric microstructure, GeoDict's acoustic simulation capabilities can be used to study the relationship between geometric structure and sound absorption performance. Typical studies include noise reduction in automotive applications, reproducing Kundt's tube tests on multi‑layer knitted fabrics in the digital model, and varying knitting parameters to optimize target sound absorption performance. This can be summarized as geometry‑dependent sound absorption properties, following the design route: knitting parameters → 3D fabric microstructure → interaction of sound waves with pore structure → sound absorption performance → reverse optimization. AcoustoDict is one of the commonly used modules listed by Math2Market for TexMath.

5. Filtration Performance and Air Permeability

The mesh density and yarn arrangement in knitted structures directly affect how fluids pass through the fabric. Filtration properties and air permeability are important application areas for TexMath. Relevant analyses include porosity analysis, the effect of mesh density on filtration efficiency, and virtual evaluation of airflow through the fabric structure. Two types of flow are considered: airflow perpendicular to the fabric plane (air passes from one side through the thickness to the other side, suitable for studying traditional permeability, filtration, and pressure drop) and airflow between fabric layers (air flows along the interior of multi‑layer or spacer fabrics, suitable for analyzing ventilation and transport behavior inside 3D spacer structures). Researchers can vary yarn size, row density, needle density, and layer spacing before manufacturing samples, and compare their effects on porosity, air permeability, and filtration performance.

6. Integration with GeoDict Modules for Multi‑Physics Performance Prediction

TexMath is positioned not merely as a tool to "draw a fabric," but to provide a 3D microstructure for subsequent digital performance experiments. Commonly used combination modules include FlowDict (for flow field, pressure drop, permeability, and air permeability), ConductoDict (for effective transport properties such as thermal and electrical conductivity), and AcoustoDict (for sound propagation and absorption). FilterDict can also be combined for filtration performance calculations. The specific modules used depend on the application. A typical GeoDict/TexMath digital design workflow is: define knitting structure and process parameters → TexMath generates 3D microstructure → analyze pore and spatial structure → compute flow and air permeability (FlowDict) → predict insulation/heat transfer (ConductoDict) → compute acoustic performance (AcoustoDict) → compare different structures → optimize design for target performance.

7. 3D Spacer Fabrics – A Typical Structure Leveraging TexMath's Strengths

3D spacer fabrics are a class of materials particularly well‑suited for TexMath. Warp‑knitted spacer fabrics typically consist of two separate fabric surface layers connected by spacer yarns. This structure offers a combination of low weight, good resilience, high flexibility, ability to withstand compressive loads, and ventilation and fluid transport space. Fraunhofer ITWM, in collaboration with TU Dresden in a DFG project, used TexMath to study the structure and properties of 3D warp‑knitted spacer fabrics, and conducted mechanical and mathematical multi‑scale modeling of fiber contacts. One of the research goals was to evaluate different structural designs through mathematical models rather than relying entirely on time‑consuming and costly physical experiments.

8. Acoustic, Filtration, and Thermal Design of Spacer Fabrics

3D spacer structures have significant inter‑layer space, making them particularly suitable for acoustic absorption, ventilation, thermal insulation, filtration, and cushioning/pressure relief. TexMath GeoApp can rapidly create multiple candidate structures by varying layer spacing, yarn diameter, and knitting density, then evaluate different designs using GeoDict's property simulation modules. For example, in acoustic applications, fabric structure can be adjusted to achieve target sound absorption; in filtration applications, mesh density can be varied to study the relationship between filtration efficiency and airflow. This approach transforms the traditional cycle of design → prototype → test → modify → re‑prototype into parametric design → digital structure generation → virtual performance testing → optimization → targeted prototyping, thereby reducing the need for extensive physical prototype screening.

9. Outlook: Simulation of Large Deformations Considering Yarn‑Yarn Contacts

The deformation of knitted materials exhibits明显的 nonlinear characteristics. This is not only because the yarn本身的 stress‑strain response is nonlinear, but also because yarns滑移 freely at contact points during loading, causing significant re‑orientation of the overall structure. Math2Market has set an outlook for simulation of large deformations considering yarn‑yarn contacts on the TexMath GeoApp page. The TexMath mechanical solver can perform tensile, shear, and bending simulations on generated knitted microstructures. Key features of its numerical approach include explicit description of sliding contacts between yarns, reduced‑order methods for computational efficiency, ability to describe significant rearrangement of knitted structures under load, and capability to couple with other physics, such as simulating fluid flow in deformed fabric structures. Important note: The mechanical simulation functionality described above currently exists in the external TexMath software, but is planned for integration into future versions of the TexMath GeoApp. At this stage, "large deformation tension/shear/bending considering yarn contacts" is not yet fully integrated as a standard feature in the current GeoDict TexMath GeoApp.

10. Relationship Between External TexMath Software and GeoDict TexMath GeoApp

TexMath originated from the fabric simulation technology developed by Fraunhofer ITWM. The external TexMath mainly includes MeshUp (fabric structure generation based on loom or knitting machine process descriptions, including woven, weft‑knitted, warp‑knitted, and spacer fabrics, describing yarn paths, loop patterns, and contact points), FiberFEM (calculating effective mechanical properties such as tensile, shear, bending, torsional, and compressive properties, using yarn cross‑section, tensile stiffness, friction, and other material properties), and FISFT (large deformation and dynamic simulation of elastic knitted fabrics, capable of describing knitting production, retraction, wearing, large deformations, and yarn contact slip, explicitly considering slip on a large number of yarn contact nodes, enabling multi‑scale simulation of larger fabric sizes). Fraunhofer TexMath also provides an interface to GeoDict, allowing fabric geometries to be used for further fluid dynamics analysis, such as calculating permeability under different stretch states.

11. Smart Electronic Textiles – Reducing Conductive Yarn Load Through Simulation

Math2Market recommends reading Developing Smart Textiles Digitally – Challenges With Knitted Fabrics, which introduces Fraunhofer's SoSeTex project. Electronic textiles integrate electronic functions such as conductive yarns, sensors, and actuators into traditional fabrics, enabling applications in active thermal insulation, sports monitoring, medical data collection, and wearable electronic devices. However, wearing, stretching, and washing all impose mechanical loads on conductive yarns and electronic connection areas. The SoSeTex project uses TexMath to build digital models to study how adjusting knitting patterns and yarn thickness can reduce mechanical stress on sensitive conductors. In related research, locally thickening yarns, changing knitting structures, and setting local reinforcement areas at circuit board connection points can all be evaluated through digital simulation before deciding whether to produce physical samples.

12. Typical Applications

Typical applications include filter media (studying porosity, mesh density, airflow, and filtration efficiency), thermal insulation materials (comparing thermal insulation performance through microstructure modeling and transport property calculations), automotive noise reduction (using AcoustoDict to compute structure‑dependent sound absorption and optimizing knitting parameters), 3D spacer fabrics (varying layer spacing and knitting structure to build 3D structures), and smart electronic textiles (using external TexMath mechanical simulation to study the mechanical stability of conductive yarns, solder joints, and areas near electronic modules).

13. Key Value of TexMath GeoApp

TexMath establishes a virtual R&D path from fabric design parameters to 3D digital structures to performance prediction. Its main features include direct generation of weft‑ and warp‑knitted structures from process and geometric parameters, support for different yarn material combinations, adjustable yarn diameter, row density, needle density, and layer spacing, support for flat knitted fabrics and 3D spacer fabrics, arbitrary repetition of periodic structures, user‑defined model spatial resolution, combination with GeoDict flow, heat/conductivity, and acoustic modules, digital evaluation of filtration, air permeability, thermal insulation, and sound absorption, and structural parameter screening and optimization before physical experiments.

14. Commonly Used GeoDict Combination Modules

The modules most frequently used in conjunction with TexMath are FlowDict for air/fluid transport and permeability, ConductoDict for effective heat transfer and thermal/electrical conductivity, and AcoustoDict for acoustic and sound absorption performance. FilterDict can also be selected for filtration performance evaluation. The appropriate module combination depends on the specific application. Note that these are not mandatory licenses for TexMath GeoApp; they are commonly used combination modules.

15. Official Page and Further Reading

For more detailed information, refer to the TexMath GeoApp Official Page – Digital Modeling of Weft‑ and Warp‑Knitted Textiles – which covers microstructure generation parameters, acoustic, filtration and air permeability applications, and the future outlook for large deformation simulation. Also recommended are Developing Smart Textiles Digitally – Challenges With Knitted Fabrics (Fraunhofer ITWM's introduction to the SoSeTex project on simulating tensile behavior of electronic knitted fabrics) and Modeling the Mechanical Properties of Knitted Spacer Fabrics (Fraunhofer ITWM's DFG project with TU Dresden on multi‑scale structural modeling of 3D warp‑knitted spacer fabrics).