Shape-morphing structured materials have the ability to transform a range of applications. However, their design and fabrication remain challenging due to the difficulty of controlling the underlying metric tensor in space and time. Here, we exploit a combination of multiple materials, geometry, and 4-dimensional (4D) printing to create structured heterogeneous lattices that overcome this problem. Our printable inks are composed of elastomeric matrices with tunable cross-link density and anisotropic filler that enable precise control of their elastic modulus (E) and coefficient of thermal expansion (α). The inks are printed in the form of lattices with curved bilayer ribs whose geometry is individually programmed to achieve local control over the metric tensor. For independent control of extrinsic curvature, we created multiplexed bilayer ribs composed of 4 materials, which enables us to encode a wide range of 3-dimensional (3D) shape changes in response to temperature. As exemplars, we designed and printed planar lattices that morph into frequency-shifting antennae and a human face, demonstrating functionality and geometric complexity, respectively. Our inverse geometric design and multimaterial 4D printing method can be readily extended to other stimuli-responsive materials and different 2-dimensional (2D) and 3D cell designs to create scalable, reversible, shape-shifting structures with unprecedented complexity.
We investigate the C-start escape response of larval fish by combining flow simulations using remeshed vortex methods with an evolutionary optimization. We test the hypothesis of the optimality of C-start of larval fish by simulations of larval-shaped, two-and three-dimensional self-propelled swimmers. We optimize for the distance travelled by the swimmer during its initial bout, bounding the shape deformation based on the larval mid-line curvature values observed experimentally. The best motions identified within these bounds are in good agreement with in vivo experiments and show that C-starts do indeed maximize escape distances. Furthermore we found that motions with curvatures beyond the ones experimentally observed for larval fish may result in even larger escape distances. We analyse the flow field and find that the effectiveness of the C-start escape relies on the ability of pronounced C-bent body configurations to trap and accelerate large volumes of fluid, which in turn correlates with large accelerations of the swimmer.
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