Recent developments in experimental path-following

The drive for lightweighting leads to thinner and thinner structures that are more prone to instabilities. Simultaneously, a renewed interest in structural instability revolves around purposefully embedding instabilities in structures to add functionality beyond structural load-carrying capability. By designing structures that behave predictably once an instability is triggered, our research aims to develop a new class of well-behaved nonlinear structures.
Advances in experimental testing of nonlinear structures are significantly lagging behind numerical methods. While numerical methods based on continuation principles such as path-following, calculation of bifurcations, branch-switching, and bifurcation tracking are now well established, nonlinear experimental methods have not advanced beyond simple displacement and force control. This means that the nonlinear response of even simple nonlinear structures cannot be fully characterised, as established techniques induce dynamic snaps at turning points and subcritical bifurcations.
We propose a testing method based on adding control points to a structure in order to: (i) stabilise otherwise unstable equilibria; (ii) control the shape of the structure; and (iii) provide information about the experimental “tangential” stiffness matrix. With this approach all the features of the numerical techniques mentioned above can (theoretically) be replicated.
The current testing method is intricately linked to a virtual testing environment that allows the experimenter to test the underlying algorithms, as well as the location and number of control points, i.e. to design the experiment. Here, we present the algorithms underlying experimental path-following, the use of virtual testing, and finally, experimental implementation on a shallow arch.