Topological Interlocking Structures (TIS) have been increasingly studied in the past two decades. However, some fundamental questions concerning the effects of Young's modulus and the friction coefficient on the structural mechanics of the most common type of TIS application – centrally loaded panels – are not yet clear. Here, we present a first-of-its-kind parametric study that aims to clarify how these two parameters affect multiple aspects of the behavior and failure of centrally-loaded TIS panels. This includes the evolution of the structural response up to and including failure, the foremost structural response parameters, and the residual carrying capacity. We find that the structural response parameters in TIS panels scale linearly with Young's modulus, that they saturate with the friction coefficient, and that the saturated response provides an upper-bound on the capacity of centrally loaded TIS panels reported in the literature. This, together with additional findings, insights, and observations, comprise a novel contribution to our understanding of the interlocked structural form.