Hierarchical Design of Shape-Memory Polymer Mechanisms With Large Deformation Kinematics

Shape-memory polymers (SMPs) are a unique class of materials that exhibit large shape changes in response to non-mechanical loading.  This capability can be harnessed to produce morphing structures and mechanisms that are activated through a controlled temperature cycle.  We present a novel hierarchical design framework for synthesis of self-actuating mechanisms that exhibit complex motion.  The framework uses three-dimensional structural topology optimization to design a set of kinematic components which form the building blocks of the mechanism.  These components contain two distinct SMP materials, each with a unique transition temperature.  The topology optimization algorithm systematically distributes the two SMP materials throughout the volume of the component. This algorithm contains a novel material interpolation scheme that is used to parameterize the two-material design space in a continuous fashion.  The algorithm also contains a time-dependent thermomechanical finite element model that predicts the displacement response of the SMP structure when subject to applied stress and thermal loads.  The optimization algorithm is powered by design sensitivities, which are computed accurately and efficiently using a path-dependent adjoint formulation.

When the topologically optimized components are subject to a thermomechanical programming cycle, they will undergo a targeted shape change that is encoded into the material distribution.  We use this technique to generate a set of specialized components that produce bending and torsional motion.  These components are then 3D-printed and subject to a thermal cycle in the laboratory in order to observe their motion and validate the topology optimization process. Precise measurement of the deformation of the components is achieved through high-resolution three-dimensional tomographic scanning of each component.  These measurements are then fed into a subsequent design synthesis program in which we use a genetic algorithm to assemble the components into a kinematic chain containing the optimal sequence of components needed to generate a desired end-configuration.  For a given sequence of components, the genetic algorithm computes the relative position and orientation the of the tip of the chain by performing a forward kinematics analysis.  The forward kinematics model computes its output based on the experimental measurements obtained for each component.  In this way, the prediction of the forward kinematics model is not subject to modeling errors associated with the finite element model.  Furthermore, the large deformation kinematics are uncoupled from the structural mechanics model used in the topology optimization algorithm.

The resulting three-stage hierarchical design framework has been implemented on a series of example problems in which we synthesize various mechanisms that assume complex shapes such as a self-tying knot.  We present both experimental and computational results for each example.