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.

The Sandia Fracture Challenges provide the mechanics community a forum for assessing its ability to predict ductile fracture through a blind, round-robin format where mechanicians are challenged to predict the deformation and failure of an arbitrary geometry given experimental calibration data. The Third Challenge, issued in 2017, required participants to predict fracture in an additively manufactured 316L stainless steel tensile-bar configuration containing through holes and internal cavities that could not have been conventionally machined. The volunteer participants were provided extensive materials data, from tensile tests of specimens printed on the same build tray to electron backscatter diffraction maps of the microstructure and micro-computed tomography scans of the Challenge geometry. The teams were asked to predict a number of quantities of interest in the response, including predictions of variability in the resulting fracture response, as the basis for assessment of the predictive capabilities of the modeling and simulation strategies. This paper describes the Third Challenge, compares the experimental results to the predictions, and identifies successes and gaps in capabilities in both the experimental procedures and the computational analyses to inform future investigations.

A process of directed UV photo-curing was previously developed for producing periodic thiol-ene lattices, with potential for use in lightweight structures. The present study probes the compressive response of two families of such lattices: with either one or two layers of a pyramidal truss structure. The principal goals are to assess whether the strengths of the lattices attain levels predicted by micromechanical models and to ascertain the role of lattice heterogeneities. These goals are accomplished through characterization of the lattice geometries via X-ray computed tomography and optical microscopy, measurements of the mechanical properties of the constituent thiolene and those of the lattices, and strain mapping on the lattices during compressive loading. Comparisons are also made with the properties of the thiol-ene alone, produced in bulk form. We find two lattice heterogeneities: (i) variations in strut diameter, from smallest at the top surface where the incident UV beam impinges on the monomer bath to largest at the bottom surface; and (ii) variations in physical and mechanical properties, with regions near the top surface being stiffest and strongest and exhibiting the highest glass transition temperature. Finally, we find that the measured strengths of the lattices are in accord with the model predictions when the geometric and material property variations are taken into account in the micromechanical models.

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Recent endeavors to combine the desirable energy-absorption characteristics of stochastic foams with the comparatively high strengths of pyramidal lattices have shown promise for creating composites that outperform their constituents alone under compressive loading. Herein we employ numerical and analytical models to identify both the mechanisms by which synergistic behavior is obtained in such composites and the constituent mass fractions that yield maximum benefits. We find that the loading boundary conditions piay a crucial role. When, for instance, composites are loaded between plates that are well bonded to the composites, their specific strengths invariably exceed those predicted by a rule-of-mixtures; however, these strengths can always be improved through an optimized lattice of equivalent mass. In contrast, when the composites are loaded betu'een frictionless plates, their specific strengths exceed not only rule-of-mixtures predictions but, in many cases, aiso that of any mass-equivalent pyramidal lattice alone subject to the same (frictionless) conditions. The origin of this behavior is found to arise from foamstabilization of lattice bending and splaying: deformation modes that govern strength in the absence of foam. In essence, the foam causes a transition from bend-dominated to stretch-dominated behavior in the lattice.