  We present a critical advance in experimental testing of nonlinear
structures. Traditional quasi-static experimental methods control the
displacement or force at one or more load-introduction points on a structure.
This approach is unable to traverse limit points in the control parameter, as
the immediate equilibrium beyond these points is statically unstable, causing
the structure to snap to another equilibrium. As a result, unstable
equilibria---observed numerically---are yet to be verified experimentally.
Based on previous experimental work, and a virtual testing environment
developed herein, we propose a new experimental continuation method that can
path-follow along unstable equilibria and traverse limit points. To support
these developments, we provide insightful analogies between a fundamental
building block of our technique---shape control---and analysis concepts such as
the principle of virtual work and Galerkin's method. The proposed testing
method will enable the validation of an emerging class of nonlinear structures
that exploit instabilities for novel functionality.
