# Modeling, Simulation and Optimization of Knitted Compression Stockings

The company BSN medical is manufacturing different products from diverse knitted fabrics, among others  tubular  knitted compression stockings. The fact that despite of the same basic design diverse models can be developed from the same material is the particular characteristic of these compression stockings.

#### The Interaction of the Materials Produces Properties

An important characteristic of design of all compression stockings is that in addition to the yarn of the construction another yarn is added; only through the interaction of both yarns the final properties come into being.

The aim of BSN Medical is to standardize and automatize the process of development that is strongly controlled by experience today. It should be possible for example that a specific compression stocking made from a newly-created material is designed virtually so that for the novel product the original characteristics of compression can be kept. Furthermore, machine parameters can be determined, to modify the compression at defined positions in case of unchanged material. Finally the possibility to design patient-speicific stockings at the computer should be created.

For this aim, ITWM developed special algorithms and implemented them into the own calculation tool TexMath:

• The numerical methods are based on the finite-element-method with non-linear truss-elements that is extended to frictional contact between yarns in this tool.
• The friction force is modelled by means of the Euler-Eytelwein law.
• The non linear problems are solved by two separate Newton procedures, for the elastic deformation and the sliding under friction force.

## Knitting Simulation

#### Virtual Stockings on a Virtual Leg

By means of this computation programme the procedure of virtual knitting of a compression stocking is simulated and presented visually using different threads and parameters of the machine during the production. The virtual stockings resulting hereof are extended again in another simulation in order to get force-strain curves for a knitted sample. The simulated force-strain curve coincides well with the measured one.

Furthermore the stocking, knitted virtually, is put on a virtual leg.This is done by means of seven measurements at seven zones of the leg along the leg’s axis. Usually, on each line between every two zones, a value of the pressure on the leg is prescribed in the norms.

#### Aim of the Project:

• The aim of this project is to reach a prescribed pressure profile for a deformed knitted fabric.  At this, in case of indicated yarn characteristics, optimal machine parameters are searched for each zone in order to minimize the deviation of tension of the stocking with regard to the targeted pressure profile