oa Fractal Folding to Develop Highly Expandable Multifunctional Lattice Structures

The properties of traditional materials are primarily determined by their atomic or molecular arrangements, which are typically difficult to modify due to constraints on sub-continuum forces in their material lattice and relatively closely packed microstructure. Engineered metamaterials, however, have been shown to allow properties that significantly expand and outperform those of the universe of existing materials. Lattice materials, whose structure is made up through tessellation of a fundamental geometrical unit cell can be seen as analogs of natural crystals and thus serve as an excellent template for metamaterial development. Abundant free space inside cellular structures make imparting real-time geometrical changes in their underlying structure much easier and since the overall properties of lattice materials are directly linked to the geometry of the underlying unit cell, it becomes possible to herald materials capable of reversible change of properties through physical stimuli. In the present work introduce a new class of lattice materials, where a controlled simultaneous folding of the lattice walls results in a significant size reduction while preserving the overall shape of the original lattice. This reversible folding scheme results in 67 and 50% reduction in size at each level for lattices with triangular and square grid topologies, respectively, while the design enables multiple levels of folding to achieve a desired final size. This high degree of geometrical and micro-structural change can yield a correspondingly wide bracket of mechanical and multifunctional behavior. We also study the elastic properties and the phononic band structure of the lattice at different stages of folding, using analytical and finite element methods. This size-changing concept provides an alternate technique for controlling the underlying topology rapidly and reversibly through simple collapse or expansion of the base lattice. Such dramatic change of size points to potential applications for deployable structures, which can simultaneously benefit from the inherent lightweight and multifunctional characteristics associated with lattice architectures.