Shape transformers for phononic band gaps tuning in two-dimensional Bloch-periodic lattice structures

A general analytical framework for the mechanics of heterogeneous hexagonal lattices

“…Several researchers proposed designs for obtaining a novel class of metamaterials with user-defined properties. The honeycomb material is being studied in an extensive manner [11][12][13][14][15][16][17][18] and utilised to manufacture structural members in the aerospace industry due to their high specific stiffness low relative density. It is also the geometric flexibility and manufacturing suitability that the hexagonal material is explored extensively.…”

Multiscale Impact Mechanics of Additively Manufactured Periodic Cellular Solids

“…There are a few papers with nonhierarchical topologies that designed their topologies with non-circular cross-sections, namely [69,[82][83][84][85][86][87], but they did not investigate the effect of any change in crosssectional shape might have on the mechanical or energy absorption response of the lattice material. Since advantages to the properties of truss-based lattices for other applications has already been in development (specifically with the use of shape transformers, detailed by Pasini [88]), further research into this area for energy absorption capabilities could yield great results [89][90][91][92].…”

“…First proposed by Pasini et al in [172] in 2003 for evaluating the structural efficiency of different cross-sections to bending, shape transformers have since inspired and been used across research interests [88][89][90]92,[173][174][175][176][177][195][196][197][198][199]. Pasini [88], who outlined the use of shape transformers for the optimum selection of lightweight beams, provided indices for material and cross-sectional shape selection to minimize mass while still maintaining a focus on stiffness.…”

“…In 2021, Gasparetto et al [89,90,199] combined shape transformers with periodic cellular solids, investigating the effect on mechanical band gap characteristics and wave propagation for the application of lattice materials in vibration filtering. In this literature they found that using shape transformers to modify the microscopic geometric beam parameters could influence the macroscopic mechanical properties of the lattice, specifically its dynamic behavior.…”

“…Area and second moment of area for solid and hollow cross-sections belonging to rectangular, elliptical, and diamond families. Adapted from [88,90,[172][173][174] 4. Shape transformers for solid and hollow derivatives belonging to rectangular, elliptical, and diamond families.…”