Abstract
One of the biggest perceived challenges in building megastructures, such as the space elevator, is the unavailability of materials with sufficient tensile strength. The presumed necessity of very strong materials stems from a design paradigm which requires structures to operate at a small fraction of their maximum tensile strength (usually, 50% or less). This criterion limits the probability of failure by giving structures sufficient leeway in handling stochastic components, such as variability in material strength and/or external forces. While reasonable for typical engineering structures, low working stress ratios-defined as operating stress as a fraction of ultimate tensile strength-in the case of megastructures are both too stringent and unable to adequately control the failure probability. We draw inspiration from natural biological structures, such as bones, tendons and ligaments, which are made up of smaller substructures and exhibit self-repair, and suggest a design that requires structures to operate at significantly higher stress ratios, while maintaining reliability through a continuous repair mechanism. We outline a mathematical framework for analysing the reliability of structures with components exhibiting probabilistic rupture and repair that depend on their time-in-use (age). Further, we predict time-to-failure distributions for the overall structure. We then apply this framework to the space elevator and find that a high degree of reliability is achievable using currently existing materials, provided it operates at sufficiently high working stress ratios, sustained through an autonomous repair mechanism, implemented via, e.g. robots.