We study the Ginzburg-Landau equations of super-conductivity describing the experimental setup of a Stiffnessometer device. In particular, we consider the nonlinear regime which reveals the impact of the superconductive critical current on the Stiffnessometer signal. As expected, we find that at high flux regimes, superconductivity is destroyed in parts of the superconductive regime. Surprisingly, however, we find that the superconductivity does not gradually decay to zero as flux increases, but rather the branch of solutions undergoes branch folding. We use asymptotic analysis to characterize the solutions at the numerous parameter regimes in which they exist. An immediate application of the work is an extension of the regime in which experimental measurements of the Stiffnessometer device can be interpreted.
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