Damage and strain identification in multifunctional materials via electrical impedance tomography with constrained sine wave solutions

Tomographic methods such as electrical impedance tomography have tremendous potential for electrical conductivity-based structural health monitoring, damage identification, strain sensing, and environmental/corrosion sensing as evidenced by a growing body of literature employing electrical impedance tomography. However, electrical impedance tomography also has important limitations preventing its widespread acceptance such as requiring burdensome computational resources not available to on-board structural health monitoring and often difficult to obtain initial estimates of conductivity distributions. We herein overcome these limitations by developing a novel electrical impedance tomography reconstruction algorithm with substantially abated computational requirements and independent of initial estimates. This method is predicated on the difference between two sets of observed voltages being due to a difference in resistivity that is constrained to be a summation of two-dimensional sine waves. This method is first explored analytically and then demonstrated experimentally on three different materials. This approach is an important advancement to the state of the art because it overcomes critical limitations of electrical impedance tomography thereby substantially facilitating the viability of electrical impedance tomography for real structural health monitoring applications.