Pyramidal Lattice Structures for High Strength and Energy Absorption

Abstract

Recent developments in directed photocuring of polymers have enabled fabrication of periodic lattice structures with highly tailorable geometries. The present study addresses the mechanics of compressive deformation of such structures with emphasis on the effects of strut slenderness L/D, strut inclination angle 9, and number of repeat lattice layers N. We present analytic models and finite element calculations for a broad parameter space and identify designs that yield desirable combinations of specific strength and energy absorption. The optimal designs (those for which crushing occurs at nearly constant compressive stress) are found to be those in which there is only one pyramidal layer, the inclination angle is of intermediate value (9 = 50 deg) and the strut slenderness ratio falls below a critical value, typically L/D = 4. The performance of near-optimal structures is attributable to the balance between two competing processes during plastic deformation: (i) geometric hardening associated with lateral expansion of the nodes and the struts, and (ii) geometric softening arising from the corresponding reduction in strut angle. Comparisons with stochastic foams show that the lattice structures can be designed to attain levels of energy absorption not possible by foams (by factors of 3-5 on a mass basis), albeit at higher stress levels than those required for crushing foams.

Effects of material heterogeneities on the compressive response of thiol-ene pyramidal lattices

“…Since the buckling stress is inversely proportional to K 2 , a change in K of this magnitude would lead to a twofold change in strength. This effect has been confirmed through recent finite element calculations on both one-and two-layer lattices [27]. The calculations further show that the inferred value of K continues to increase as the number of layers is increased, eventually reaching 1.…”

“…In the strut regions, the shear strains in the local coordinate systems, defined by the strut axes, were very close to zero before buckling, confirming that the struts experience essentially axial loading. This feature is also obtained from finite element analyses of these lattices [27]. The distribution in cross-sectional area of the struts is shown in Fig.…”

“…An assessment of the measured strengths has been made using models of yielding and buckling of periodic lattice structures [27]. First, a standard statics analysis is used to obtain the axial stress borne by the struts, assuming that loads are transmitted via axial compression.…”

Influence of processing conditions on strut structure and compressive properties of cellular lattice structures fabricated by selective laser melting

“…Some tests were also interrupted at different stages of compression and the specimens examined by SEM to study the deformation and fracture mechanisms of the lattice structures. The compression strengths are expressed in several different ways, including the nominal engineering strength (the maximum load divided by the cross sectional area of the lattice structure) reflecting the load bearing capacity of the structure and the effective metal strength (the maximum load divided by the cross sectional area occupied by the struts (A) which is given by [27]). …”

A piezo-shunted kirigami auxetic lattice for adaptive elastic wave filtering

“…In this paper, we numerically investigate a strategy for controlling directionality properties of a kirigami auxetic lattice with the pyramidal topology described in [54]. Pyramidal lattices have been developed in recent years as lightweight cores for energy absorption [58,59,60] and unusual stretchable-bendable composites [61]. Concerning the kirigami pyramidal lattice of reference [54], the unusual deformation properties and its wave propagation characteristics are also due to the fact that the system is only partially auxetic [62], i.e., it exhibits auxetic behaviour only in the xy and yx planes.…”