The effects of five different types of imperfection (fractured cell walls, missing cells, cell wall waviness, cell wall misalignment, and non-uniform cell wall thickness) on actuation performance are numerically investigated for the Kagome lattice and two of its variants: Double Kagome (DK) and Kagome with concentric triangles (KT). The lattice materials of interest are excited by deploying a single linear actuator located at their centre. The actuation performance of the lattices is determined by measuring the energy spent by the actuator and the attenuation distance of the deformation induced by the actuator. The deformation localises in a narrow corridor approximately one unit cell-wide for all three lattices in the absence of imperfections. The finite element calculations show that the critical parameter determining the actuation performance is the stiffness along the actuation corridor rather than the macroscopic Young's modulus of the lattice. The less stiff the actuation corridor is, the smaller the actuation energy and the larger the attenuation distance (except when there is a fractured or wavy cell wall or a missing cell along the actuation corridor that immediately attenuates the displacement field). When imperfections are randomly distributed outside the actuation corridor, cell wall misalignment and non-uniform cell wall thickness barely affect the actuation performance, although cell wall misalignment considerably reduces the macroscopic Young's modulus of the lattice. The actuator feels the presence of fractured or wavy cell walls or missing cells, whether placed inside or outside the actuation corridor. These three types of imperfection cause the largest knock-down both in the macroscopic Young's modulus of the block and the actuation energy while increasing the attenuation distance. The increase in the attenuation distance due to imperfections is, however, impotent, as the accompanying reduction in stiffness makes the lattice more vulnerable to failure. However, if a defect is introduced slightly beyond the attenuation distance of the perfect lattice as an intentional design feature, it is beneficial for the actuation performance without decreasing the macroscopic Young's modulus.

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The Kagome structure has been shown to be a highly suited micro-architecture for adaptive lattice materials, in which selected lattice members are replaced by actuators aiming to create shape morphing structures. It is the combination of in-plane isotropy, high stiffness and low energy requirement for actuation that makes the planar Kagome structure the best performing micro-architecture known to date. Recently, Pronk et al. (2017) have proposed a set of topological criteria to identify other micro-architectures suitable for actuation. In the present paper, four novel lattice topologies are presented which were contrived in light of these criteria. Matrix analysis is performed to reveal the static and kinematic properties of the pin-jointed versions of these four structures. The finite element method is used to determine their stiffness and actuation characteristics. One of the proposed designs is found to match the optimal elastic properties of the Kagome structure, while it requires less energy for (single member) actuation. However, the displacement field induced by actuation attenuates faster than in a Kagome lattice. The presented results also show that the criteria proposed by Pronk et al. (2017) should be refined in two regards: (i) statically indeterminate lattice materials do not necessarily result in high actuation energy and thus should not be ruled out, and (ii) as shown by counterexample, the criteria are not sufficient.

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In the last two decades, lattice materials have received considerable attention as a means to design adaptive (shape morphing) structures [1-5]. Similar to foams, lattice materials are lightweight, but can be much stiffer and stronger depending on their microarchitecture. Externally triggered lengthening or shortening (actuation) of one or more members in a lattice material can be used to achieve significant macroscopic shape change.@en

The structural symmetry of a material can be manifested at a multitude of length scales such as spatial arrangement of atoms in a crystal structure, preferred orientation of grains in a polycrystalline material, alignment of reinforcing particles/fibers in composites or the micro-architecture of members in cellular solids. This paper proofs, in a simple yet rigorous manner, that six axes of fivefold structural symmetry is necessary and sufficient for isotropy of the elastic moduli tensor in the three-dimensional (3D) context.

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In the last two decades, most of the studies in shape morphing technology have focused on the Kagome lattice materials, which have superior properties such as in-plane isotropy, high specific stiffness and strength, and low energy requirement for actuation of its members. The Kagome lattice is a member of the family of semi-regular tessellations of the plane. Two fundamental questions naturally arise: i-) What makes a lattice material suitable for actuation? ii-) Are there other tessellations more effective than the Kagome lattice for actuation? The present paper tackles both questions, and provides a clear answer to the first one by comparing an alternative lattice material, the hexagonal cupola, with the Kagome lattice in terms of mechanical/actuation properties. The second question remains open, but, hopefully easier to challenge owing to a newly-discovered criterion: for an n-dimensional (n=2,3) in-plane isotropic lattice material to be suitable for actuation, its pin-jointed equivalent must obey the generalised Maxwell's rule, and must possess M=3(n−1) non strain-producing finite kinematic mechanisms.@en