Size effect anomalies in the behaviour of loaded 3D mechanical metamaterials

Abstract

Size effects exhibited by mechanical metamaterials when loaded may be positive such that reducing overall size towards that of the length scale of the underlying structure intrinsic to the material is accompanied by increasing stiffness or rigidity, a phenomenon that has been repeatedly observed and is also forecast by various more generalized continuum theories of deformation in loaded heterogeneous continua. However, such effects may in certain circumstances be contradictory in that decreasing size is accompanied by increasing compliance, the transition from the conventional, positive to this theoretically unanticipated negative behaviour having been explained recently in terms of the distribution of material within 2D continua subject to bending. Here we report on a novel phenomenon newly observed in periodic 3D lattice materials comprised of repeated cubic unit cells formed of exterior edge and interior diagonal connectors. Subtle redistribution of matrix material from edges to diagonals causes the size effect to change dramatically, inverting from positive to negative when loaded in the torsional mode while the corresponding effect for the flexural mode remains entirely positive under the same circumstances. This observation may lead to the prospect of optimising the design of 3D periodic metamaterials to provide a stiffer response in one loading mode and a more compliant response in another, a feature that could potentially be exploited in various innovative applications.

On the question of the sign of size effects in the elastic behavior of foams

“…For meta-materials, a positive size effect in bending has been reported also by Dunn and Wheel [9] as well as by Waseem et al [43] and Rueger and Lakes [35,36,38,39]. Though, this effect in regular mesostructures can be explained by the shift of material away from the neutral axis [27,45,47] according to Steiner's theorem.…”

Bending characteristics of carbon nanotubes: Micropolar elasticity models and molecular dynamics simulations

“…It should be noted that although Eq. ( 20) may not be exact, a similar approach with the same constraint is proposed by Lake [107] for the bending rigidity of a micropolar beam with rectangular cross section which is further adopted in various studies [126][127][128][129]. An even more simplified version of this formulation neglecting χ yz is also used by some other researchers [130][131][132].…”

A Review on Tailoring Stiffness in Compliant Systems, via Removing Material: Cellular Materials and Topology Optimization

“…Most recently, in [111] a 2D kagome honeycomb was optimized for delivering high amplitude actuation. In the same year, Dunn et al [112] demonstrate that changing the cell size in lattice materials might involve maximizing stiffness in one mode while minimizing it in another.…”