# Monitoring the Joint Area of Composite Membrane Materials
## 2 Materials and Methods
### Methods
#### 2.2.6 Numerical Modelling and Simulation of Membrane Joints  
A structurally integrated thread with conductive properties can be used to examine the local strain of a technical membrane surface under load. To validate the results obtained from this structural sensor system, numerical analysis accompanies these developments. Virtual investigations based on finite element analysis (FEA) can be used to clarify uncertainties. Whereas physical tensile tests, as seen in Figure 3, provide information on the global tensile strain, the local strain situation in the joint areas of membranes remains unknown. To obtain information on local tensile strain, a numerical tensile simulation was performed to define the precise membrane material properties as well as the membrane-to-membrane connection behavior including shear and peeling failure modes. The textile-reinforced membrane material was modelled by 2D shell elements using the commercially available FEA-Software LS-DYNA(r), whereas the sensor thread was modelled by use of truss elements. In this regard, bending properties were neglected to account for the low bending stiffness being a typical characteristic of textile fibers and threads. A nonlinear orthotropic material model was applied to the shell elements. A picture of the finite element model is shown in Figure 5.  
The membrane material was tested according to Section 2 to obtain the membrane tensile properties for both main reinforcement directions. A nonlinear orthotropic material model was adapted to account for the examined behavior, which is common for textile reinforced membranes. As mentioned before, this model serves to investigate the local strain field, which cannot be evaluated based on the physical tensile test, as described in Section 2.2.4. However, since the sensor thread will operate at the local level, information on the local strain situation is crucial for dimensioning and evaluating the entire sensor system. Through a numerical simulation, information on local strain during loading and after failure can be gained.  
To examine the interaction between sensor thread and membranes in the joint area, different contact properties were considered within the model. As illustrated in Figure 5, the sensor thread was  
Figure 4: Layout of the strain sensor.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Number of Sensor Loops** & **n** & **10** \\ \hline Length of the sensor loops & 1 [mm] & 18 \\ \hline Width of the sensor loops & a [mm] & 4 \\ \hline Width of the sensor & b [mm] & 40 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Sensor dimensions.  
stitched onto only one of the joining partners, whereas the package of sensor thread and membrane was welded onto the second membrane. To cover this situation within the numerical simulation, contact conditions were chosen according to Figure 6.  
The sensor thread was stitch bound onto the first membrane. Hence, a failure of this contact was not considered. The two membrane joints themselves were bound by a failure contact, which included failure stress in shear and peel loading conditions. Therefore, a change in or failure of membrane-to-membrane contact was transferred to the sensor load level. The failure criterion was a given level of maximum stress in the contact elements, which could not be exceeded. After an initial failure, the contact elements ensure a standard body-to-body contact. A tied-bound contact situation is not to be created anymore. The input values for the failure criterion were obtained from physical tests, as described in Section 2.2.4.