Modeling of embedded impedance sensors for deformation detection in glued wood

Embedded impedance-based sensors printed on highly permeable substrates have recently been introduced for monitoring the curing and cross-linking processes of adhesives in glued wood structures. Although these sensors are primarily designed for in-process monitoring during manufacturing, their capacitive response in the fully cured state is influenced not only by material properties but also by the geometry of the sensor. This geometric sensitivity suggests that such sensors may also be suitable for deformation detection in glued wood structures. The objective of this thesis is to develop a modeling framework that relates mechanical deformation of laminated wood structures to changes in the electrical response of embedded printed impedance sensors. To this end, the theoretical foundations of continuum mechanics and electromagnetic field theory are reviewed, and appropriate variational formulations are derived. The two physical fields are treated in an unidirectional manner, such that the mechanical and electrical problems are solved sequentially. The mechanical problem is discretized using a mixed finite element method, while the electrical problem is formulated within a classical finite element framework. The proposed framework enables the computation of deformation-dependent impedance responses. Numerical calculations are performed for representative loading scenarios and are compared with experimental measurements. In addition, a reduced-order modeling approach based on the plane-stress assumption is investigated with respect to its suitability for calibration purposes using a representative unit cell of the three-dimensional structure. The presented framework provides a foundation for the further development of embedded impedance sensors towards applications in structural health monitoring of glued wood.