Hybrid optimization schemes for solving the piezoresistive inversion problem in self-sensing materials

Materials with electrically conductive nanofillers have the ability to 'sense' changes to their mechanical state. When these materials are deformed, the embedded nanofiller networks are disturbed causing a measurable change in the electrical conductivity of the material. This self-sensing property, known as piezoresistivity, has been leveraged in numerous engineering venues. Although this property has been thoroughly explored, prevailing self-sensing techniques provide little-to-no information about the underlying mechanical state of the material, such as the displacement and strain. This information must be indirectly obtained from the conductivity change. This limitation exists because obtaining mechanics from conductivity is an under-determined inverse problem with many possible mathematically feasible solutions. Previous work in this area used metaheuristic algorithms and imposed mechanics-based constraints to solve the piezoresistive inversion problem. Although this approach was successful, it was computationally inefficient due to the stochastic search process and the need to perform multiple searches to find a converged solution. To overcome this limitation, we herein propose a hybrid optimization scheme for solving the piezoresistive inversion problem. This scheme is implemented in two steps. In the first step, a metaheuristic algorithm performs a single search for a suitable solution to the inverse problem. In the second step, a gradient descent algorithm searches for the final solution using the solution from the previous step as the starting point. We explore different norms for the fitness function of the metaheuristic search and demonstrate using experimental data that the proposed hybrid optimization scheme can accurately and efficiently calculate displacements and strains from conductivity changes. This exploration significantly advances the state of the art by enabling computationally efficient and highly accurate predictions of full-field mechanical condition in self-sensing materials for the first time, thereby paving the way for greater use of these principles in practice.