How to efficiently bend straws: Nudged elastic band-based method for minimally actuated targeted reconfiguration

We introduce a numerical framework for minimally actuated reconfiguration of mechanical structures that are characterized by rich multiaxial multistability, focusing on ‘bendy straw’-inspired elements. These elements, which are referred to as ‘straws’ for short, are modeled as arrays of unit cells, each having up to four multiaxial stable equilibria in the planar case discussed here, which overall provides the straw with a myriad of complex stable configurations. We lay out the theoretical foundation and introduce a numerical scheme (the ‘forward model’) to describe the nonlinear mechanical behavior of a single straw with spatially varying or uniform unit cells, under prescribed relative translational and rotational displacements between its ends. We show that the uniaxial behavior of a nonuniform straw can be predicted by a simple static analysis, which under certain analytically formulated design conditions admits finding the actuation path needed to create a wanted uniaxial reconfiguration. To predict the planar motion during multiaxial actuation and to allow for a large variety of admissible reconfigurations, we introduce a more complex nudged elastic band (NEB)-based algorithm. The latter seeks the energetically optimal prescribed displacements that must be applied to the displacement-controlled end of a cantilevered straw for a general-target multiaxial reconfiguration. For validation, the actuation paths extracted from the algorithm for different benchmarks are simulated using the forward model, which ensures the achievement of the targeted reconfigurations.