Main code for difference image with L2 regularization. from Full-field mechanics imaging by direct inversion of electrical data

Self-sensing materials with deformation-dependent electrical conductivity have been studied in diverse applications. A limitation of self-sensing materials is that they do not directly report on the underlying condition of the material. That is, it would be much more useful to know the actual stresses, strains or damages that give rise to observed conductivity changes. The process of deducing material condition from electrical data is called the <i>self-sensing inverse problem</i> (SSIP). Previous work has required electrical impedance tomography (EIT) as an intermediate step to estimate the conductivity distribution prior to estimating the spatially varying mechanics. But this is undesirable because EIT is an ill-posed inverse problem and is highly dependent on regularization, which renders the SSIP as subject to the same assumptions and limitations of EIT. The contribution of this manuscript is the development of a <i>direct</i> SSIP formulation that omits the EIT step such that mechanics are predicted directly from voltage–current data. The effects of regularization type, regularization norm and formulation (difference versus absolute imaging) are also explored. The direct SSIP formulation is experimentally validated on a soft carbon nanofibre-modified polyurethane pressure sensor and compared to ANSYS-solved mechanics with good agreement.