## 4 Numerical Simulation and Experimental Work
### Numerical Simulation  
Conceptually, the capacitive method is straightforward. The electrodes provide an electric field distribution when an AC voltage is applied between the driving and sensing electrodes. The presence of the specimen and any variation in its properties (such as the presence of a defect) within the area covered by the electric field will change the field pattern distribution. A distortion in the electric field causes a change in the charge induced in the sensing electrode, and this change in the charge can be used for defect detection purposes [7]. The resulting signal is sent to standard instruments such as charge amplifiers that increase the signal-to-noise ratio (SNR) and allow small changes in the signal to be recorded, processed and outputted as a DC voltage. Since the presence of delaminations, cracks and other imperfections changes the electric field distribution in various distinctive ways, a basis for detecting defects can be established [5]. In order to understand the way electric field distributions are produced by the electrodes, and to identify how they may interact with the materials of interest, it was felt important to model the expected behavior. In this paper, we want to demonstrate the distribution of the electric field and how changes in the specimen might affect the output. Finite element (FE) modeling enables valuable information (such as visualization of the results) to towards analyzing the performance of the capacitive sensor more easily. Although finite element methods are well established in engineering calculation, care must be taken to secure suitable mesh densities in critical regions, in particular near to the source of field singularities [21]. The major source of errors is the discretization processes of the conductor segments bordering different dielectrics and of the dielectric interfaces. However, there is no need to do the complicated mathematical process in order to simulate the defects in the samples in the finite element method. This is a useful tool for predicting the fields from capacitive electrodes and how these fields are likely to interact with different materials and defects [5; 22]. Therefore, finite element (FE) modeling has been employed to predict the distribution of the electric field from capacitive electrodes and signal changes that are likely to be generated under experimental conditions. Theoretical simulations were conducted using COMSOL(tm) Multiphysics FE package, and using its AC/DC module, electric currents (ec)-type, which can be used to model the distribution of the electric field in different situations. The purpose of this analysis is to observe the field distribution and the variation of electric field strength as a function of the sample properties such as existing defects and depths of a defect. The electric field distribution for all situations has been analyzed using a three-dimensional (3D) finite element method. In this model, the driving and sensing electrode were driven by a \(+5.0\) V and \(-5.0\) V, respectively, with a 100 kHz sinusoidal signal. The shielding plate and guard electrode were set to ground potential. Based on this, there is an electric field between the positive and negative electrodes and the electric field distribution is formed in the local region in  
Figure 3: (**a**) Photograph of the pair of triangular electrodes and (**b**) Diagram of the capacitive sensor as viewed from the top surface. the specimen under the electrode pair and the liftoff between the sample and probe. A pair of a coplanar triangular electrode is placed above the surface of a specimen with 1.0 mm liftoff, and the setup is enclosed in a 120 mm \(\times\) 120 mm \(\times\) 120 mm block centred at the point (\(x=0\), \(y=0\), \(z=0\)). This block was a zero-charge boundary airbox and defined to be the computational domain, as shown in Figure 4a. A physics-controlled mesh was used and the mesh generation density is set to \"Finer\".