Strain field imaging by applying anisotropic electrical impedance tomography on conductive surface coating

Figure 1.  Left: schematic representation of the domain in the elasticity FEM simulation. The top edge of the domain was imposed a uniform displacement $ u_0 $ in the $ y $-direction, while the bottom edge was fixed in place. The edges marked in blue were assigned the condition of zero traction. Right: Finite element mesh used in the elasticity FEM simulation

Figure 2.  The components $ \varepsilon_{xx} $, $ \varepsilon_{yy} $ and $ \varepsilon_{xy} $ of the strain $ \varepsilon $ obtained from the FEM simulation, visualized within the EIT sensing region

Figure 3.  EIT FEM meshes used for modeling the synthetic data (left) and in inversion (right). The electrodes boundaries are marked in red and magenta dots

Figure 4.  Results of simulation studies. True, synthetic distributions of $ \sigma $, $ s_{xx} $, $ s_{yy} $ and $ s_{xy} $ (top row, from left to right), and NLD-based EIT reconstructions of the respective distributions in the smaller noise case ($ d_1 $ = 0.01, middle row) and larger noise case ($ d_1 $ = 0.1, bottom row)

Figure 5.  Simulation study; the larger noise realization case: Approximate posterior standard deviations corresponding to (from left to right) $ \sigma $, $ s_{xx} $, $ s_{yy} $ and $ s_{xy} $

Figure 6.  Schematic illustrations of the plane strain experiment (left) and the contact pressure experiment (right). The numbering of the electrodes is indicated in red

Figure 7.  Left: Photograph of the experimental setup in the strain experiment. The insulating rubber mat is brown and the dark square shaped area on top of it is formed by the conductive paint. Right: The region of interest (white) on which the strain was reconstructed using DIC, superimposed on the grayscale photograph of the sample

Figure 8.  Plane strain experiment. DIC based reconstructions of the strain field components $ \varepsilon_{xx} $ (left column), $ \varepsilon_{yy} $ (middle column) and $ \varepsilon_{xy} $ (right column) corresponding to three values of percentual elongation of the mat: 0.1 % (top row), 1.5 % (middle row) and 3 % (bottom row). On the top row, regions of interest, each made up of a union of two parts are marked by colored squares. Each color corresponds to one region of interest: the region ROI1 is made up of the black squares, ROI2 of the magenta squares and ROI3 of the orange squares. The side length of each square was 1 cm

Figure 9.  Plane strain experiment. EIT reconstructions for the anisotropic conductivity multiplier field components $ s_{xx} $ (left column), $ s_{yy} $ (middle column) and $ s_{xy} $ (right column) corresponding to three values of percentual elongation of the mat: 0.1 % (top row), 1.5 % (middle row) and 3 % (bottom row). Note the subtraction of unity from $ s_{xx} $ and $ s_{yy} $

Figure 10.  Plane strain experiment. Top row: EIT reconstructions of the isotropic initial conductivity $ \sigma $ given by the NLD reconstruction approach, when the $ I_1 $ dataset corresponds to the undeformed sample, and the $ I_2 $ dataset corresponds to three different deformations of the sample: 0.1 %, 1.5 %, 3 %. Bottom row: Respective estimates of the contact impedances at the initial state ($ z_1 $) and after the deformation ($ z_2 $)

Figure 11.  Left: the average values of $ s_{xx} $ (blue) and $ s_{yy} $ (red) in the region of interest $ ROI1 $ as a function of the applied elongation. The solid markers correspond to the extension phase of the experiment. Empty markers correspond to the recovery phase, in which the tension of the sample was relaxed in steps. The averaging is over the entire region of interest ROI1, made up from two parts on the left and right side of the central hole. Right: the corresponding average values for $ s_{xy} $ in the region of interest ROI1

Figure 12.  Left: Average value of $ s_{xx} $ vs. average value of $ \varepsilon_{xx} $ (blue), and average value of $ s_{yy} $ vs. average value of $ \varepsilon_{yy} $ (red) within ROI1 during the strain experiment. Right: Average value of $ s_{xy} $ vs. $ \varepsilon_{xy} $ within ROI1 (black), ROI2 (magenta) and ROI3 (orange) during the strain experiment. In both figures, the solid markers correspond to the extension phase of the experiment. Empty markers correspond to the recovery phase, in which the tension of the sample was relaxed in steps

Figure 13.  Reconstructions of the multiplier field $ s $ in the contact pressure experiment. Left column: $ s_{xx}-1 $, middle column: $ s_{yy}-1 $, right column: $ s_{xy} $. The true positions of the weight in four test cases (rows 1–4) are marked with black circles

Figure 14.  Contact pressure experiment. Top row: EIT reconstructions of the isotropic initial conductivity $ \sigma $ given by the NLD reconstruction approach, when the $ I_1 $ dataset corresponds to the undeformed sample, and the $ I_2 $ dataset corresponds to three different weight locations. The true positions of the weight are marked with black circles. Bottom row: Respective estimates of the contact impedances at the initial state ($ z_1 $) and after the deformation ($ z_2 $)