Adaptive stiffness in lattice structures through passive topology morphing

Structures with adaptive stiffness characteristics present an opportunity to meet competing design requirements. One approach to achieve this stiffness adaptivity is through topology reconfiguration. Here, the potential of using passive topology changes to achieve desired adaptivity is explored in three lattice structure designs. The first investigation involves a planar sinusoidal lattice with rectangle-like unit cells. Under sufficient compression, the cell walls bend and contact neighbouring cells. This self-contact establishes new load paths, thus resulting in kagome-like unit cells that exhibit an approximate four-fold increase in compressive and shear stiffness. The role of key geometric and stiffness parameters in critical regions of the design space is explored through a parametric study. Second investigation explores the bilinear elastic behaviour in cylindrical sinusoidal lattices. The topology transformation leads to an approximately four-fold in-crease in stiffness under compression. The lattice exhibits negative Poisson’s ratio with a step-change from ≈ −0.66 to ≈ −0.23 prior to and during contact formation, respectively. After contact formation, it displays a nonlinear Poisson’s ratio behaviour. A comparison with planar lattices reveals that cylindrical lattices exhibit bilinear behaviour for a wider range of geometric parameters. The third lattice utilizes simultaneous tensile buckling of unit cells to induce topology change. Under tension, the lattice transitions from a rectangle-like to a triangle-/pentagon-like unit cells with a seven-fold increase in stiffness. The initial and the new topologies are dominated by membrane effects. During the transformation phase, negative stiffness accounts for approximately 82% of the total elastic deformation. Experimental observations of prototypes, either 3D-printed or fabricated, show excellent correlation with finite element analysis. The analytical results provide valuable insights into the observed behaviours. The non-linear responses demonstrated by these proposed concepts may offer designers a new approach to tailor elastic characteristics</p

Topology morphing lattice structures

Planar cellular lattice structures subject to axial compression may undergo elastic bending or buckling of the unit cells. If sufficient compression is applied, the columns of adjacent cells make contact. This changes the topology of the lattice by establishing new load paths. This topology change induces a corresponding shift in the effective stiffness characteristics of the lattice – in particular, the shear modulus undergoes a step-change. The ability to embed adaptive stiffness characteristics through a topology change allows structural reconfiguration to meet changing load/operational requirements efficiently. The concept, of topological reconfiguration, can be exploited across a range of length scales, from (meta-)materials to components. Here we focus on macroscopic behaviour presenting results obtained from finite element analysis that shows excellent correlation with the observed response of 3D-printed PLA lattices. Through a parametric study, we explore the role of key geometric and stiffness parameters and identify desirable regions of the design space. The non-linear responses demonstrated by this topology morphing lattice structure may offer designers a route to develop bespoke elastic systems. </p

Bilinear stiffness and bimodular Poisson’s ratio in cylindrical sinusoidal lattices through topology morphing

Bilinear elastic behaviour allows structural designs to respond in either a stiff or compliant manner depending on the load. Here a cylindrical sinusoidal lattice structure is described that stiffens beyond a certain load. When subjected to axial compression, the lattice can undergo a topological transformation by forming contact connections. This topology change involves a transition from rectangular-like unit cells to kagome-like unit cells, associated with an approximately fourfold increase in stiffness. The lattice exhibits negative Poisson’s ratio with a step-change from ≈ −0.66 to ≈ −0.23 prior to and during contact formation, respectively. After contact formation, it displays a nonlinear Poisson’s ratio behaviour. The mechanics underpinning these behaviours are analysed using a combination of experiments and numerical modelling. A comparison with similar planar lattices reveals the effect of the global topology of the lattice (e.g. planar, cylindrical) on the unit cell-level topology morphing. The proposed topology-morphing cylindrical sinusoidal lattice introduces new design possibilities in the application-rich context of tubular structures with nonlinear mechanical properties.</p

Topology morphing in lattice structures through tensile buckling

Incorporating, by design, tensile buckling into the macroscopic response of lattice structures offers a novel approach for adaptive (meta-)material/structure development. In this study, we explore the potential of utilizing the simultaneous tensile buckling of adjacent cells to induce a transformation in lattice topology. Unit cells are passively transformed from rectangle-like to triangle/pentagon-like unit cells, with an associated change in the effective macroscopic properties. This approach provides a new route to elastically tailor the non-linear response of (meta-) materials/structures. The paper explores the behavior of such a system through finite element analysis. The results identify: i) that the initial lattice internal topology (rectangular) is dominated by membrane effects, ii) a negative region of stiffness is associated with the transformation phase, and iii) once formed, the new topology (triangular/pentagonal) exhibits positive stiffness in both compression and tension.</p

Adaptive stiffness in lattice metastructures through tensile-buckling inspired topology morphing

This paper explores the use of simultaneous tensile buckling of unit cells to induce a transformation in lattice topology. Under tension, unit cells undergo passive transformation from a rectangle-like to a triangle-/pentagon-like topology, with an associated change in the effective stiffness properties. This behaviour is investigated through finite element analysis and experiments, with analytical results providing insights into the observed behaviour. The analysis identifies (i) that the initial unit cell topology (rectangular) is dominated by membrane effects, (ii) the transformation phase is associated with negative stiffness, and (iii) once formed, the new topology (triangular/pentagonal) exhibits increased stiffness in both compression and tension. Finite element analysis confirms that the unit cell behaviour is also preserved in lattices. Under tension, the lattice undergoes a seven-fold increase in stiffness as it transitions from its initial to the new topology, with a regime of negative stiffness during this transformation accounting for approximately 82% of its total elastic deformation. This new approach to elastically tailor the nonlinear response of (meta-)materials/structures has the potential to contribute to the development of novel tensile energy absorbers.</p

Stiffness tailoring in sinusoidal lattice structures through passive topology morphing using contact connections

Structures with adaptive stiffness characteristics present an opportunity to meet competing design requirements, thus achieving greater efficiency by the reconfiguration of their topology. Here, the potential of using changes in the topology of planar lattice structures is explored to achieve this desired adaptivity and observe that lattice structures with rectangle-like unit-cells may undergo elastic buckling or bending of cell walls when subject to longitudinal compression. Under sufficient load intensity, cell walls can deform and contact neighbouring cells. This self-contact is harnessed to change the topology of the structure to that of a kagome-like lattice, thereby establishing new load paths, thus enabling enhancement, in a tailored manner, of the effective compressive and shear stiffness of the lattice. Whilst this phenomenon is independent of characteristic length scale, we focus on macroscopic behaviour (lattices of scale ≈ 200 mm). Experimentally observed responses of 3D-printed lattices correlate excellently with finite element analysis and analytical stiffness predictions for pre- and post-contact topologies. The role of key geometric and stiffness parameters in critical regions of the design space is explored through a parametric study. The non-linear responses demonstrated by this topology morphing lattice structure may offer designers a new route to tailor elastic characteristics.</p