Experimentally Probing Unstable Equilibria

In structural mechanics, the stability of structures is of paramount importance. A characteristic of structural stability is that simple structures can give rise to unexpectedly complex behaviour; this makes the phenomena both fascinating and dangerous. Traditionally, the focus in engineering has been on preventing buckling due to its potentially catastrophic effects. However, in recent years the focus has shifted towards exploiting the potential benefits of buckling -- large displacements, increased load-bearing capacity, and multifunctionality, to name a few.

Significant research effort has been expended to produce analytical and numerical methods and models which adequately capture the behaviour of unstable structures. Experimental methods, on the other hand, have received comparatively little attention. So much so that some classic 1980s Finite Element Analysis (FEA) benchmarks remain unverified by experiment. This lack of experimental methods is understandable; analytical methods can probe the solution space and perturb equilibria with relative ease, but these operations do not translate easily into a physical experiment. The vast majority of engineering testing uses displacement- or load-controlled uniaxial test methods, which fail to capture all but the simplest structural behaviour.

Our aim in this work is to develop experimental methods which emulate the family of numerical path-following techniques pioneered by Riks. Path-following (also known as numerical continuation) can capture the full response of a structure, including unstable loops in the load-displacement response. An "experimental continuation" technique will give researchers a platform to validate concepts generated by FEA, and bring these one step closer to implementation. We present the first step towards such a technique, in which we have experimentally located unstable equilibria of a shallow arch which are not accessible by traditional testing.