Topology optimisation of additively manufactured lattice structures

Abstract

Additive manufacturing allows lattice-filled structures with graded stiffness and local load-path control, but topology-optimised designs often lose performance when converted into printable struts, overhang-safe cells, and as-built geometries. We present a multiscale topology optimisation workflow for laser powder bed fusion AlSi10Mg lattice structures and validate it using compression coupons and load-bearing bracket specimens. A density-based compliance optimisation generated the macroscale material distribution, which was then mapped to manufacturable octet-truss and gyroid unit cells using homogenised stiffness libraries, minimum-feature filters, overhang constraints, and powder-removal rules. X-ray computed tomography was used to quantify as-built strut diameter, node swelling, missing members, and trapped powder before mechanical testing. For a benchmark cantilever bracket, the optimised graded octet design reduced mass by 34% relative to a stress-constrained solid topology-optimised baseline while retaining 91% of its measured stiffness; compared with a uniform-density lattice at equal mass, it increased stiffness by 22% and peak load by 17%. Finite-element predictions based on nominal geometry overestimated stiffness by 13%, but CT-corrected geometry reduced the error to 5.4%. Gyroid infill improved fatigue initiation life by approximately 1.8x relative to octet infill at the same mass, at the cost of 9% lower quasi-static stiffness. The results show that topology optimisation and lattice dehomogenisation are useful for AM only when printability and as-built geometry are treated as first-order design variables rather than post-processing checks.

Introduction

Topology optimisation has become a standard computational route for distributing material efficiently under mechanical constraints. The homogenisation formulation of Bendsøe and Kikuchi [1] and later density-based implementations such as the SIMP method made compliance minimisation accessible for engineering design [2]. Subsequent filters, projections, and length-scale constraints helped remove checkerboarding, mesh dependence, and grey-scale ambiguity [3,4,5]. These developments are central to modern lightweight design, but they do not by themselves produce parts that can be printed, cleaned, inspected, and qualified.

Additive manufacturing changes the optimisation problem because it relaxes some traditional machining constraints while introducing new ones: minimum wall and strut diameter, unsupported overhangs, build orientation, heat accumulation, surface roughness, trapped powder, and process-induced anisotropy [6]. Several studies have therefore argued that topology optimisation and additive manufacturing must be bridged by explicit manufacturing constraints rather than by manually editing an optimal density field after the fact [7,8]. Lattice structures are an appealing bridge because their cell size and relative density can vary locally, allowing smooth transitions between load paths while maintaining open porosity for powder removal and inspection [9,17].

The mechanics of lattices are well understood in idealised form. Stretch-dominated architectures such as the octet truss can achieve high stiffness and strength at low relative density [10], while cellular-solid scaling laws explain why bending-dominated cells are more compliant and more damage tolerant in some regimes [11]. Printed lattices, however, depart from ideal truss models. Laser powder bed fusion can produce strut undersizing, node swelling, rough surfaces, partially fused particles, and orientation-dependent defects. Mechanical tests of selective-laser-melted and polymer-printed lattices show that geometry, process, and material must be interpreted together [12,13,14,15].

This study develops and tests a workflow for topology-optimised lattice structures fabricated by laser powder bed fusion. The purpose is not to claim a universal lattice architecture. Instead, we ask how much of the numerical topology-optimisation benefit survives after the design is converted into manufacturable unit cells and printed in AlSi10Mg. The work combines density optimisation, homogenised lattice libraries, printability filters, X-ray computed tomography, quasi-static testing, and limited fatigue testing.

Design problem and optimisation workflow

Two benchmark components were studied. The first was a rectangular compression block used to compare uniform and graded lattices under nominally simple loading. The second was a cantilever bracket with two bolt holes, one bearing pad, and a 4.2 kN design load applied 86 mm from the mounting plane. The bracket envelope measured 140 mm by 92 mm by 58 mm. A solid topology-optimised baseline was generated using the same load cases, boundary conditions, and material volume as the lattice designs, then smoothed and thickened to satisfy the same minimum wall rule.

The macroscale optimisation used a density-based compliance objective with a 35% volume fraction for the bracket and 30% for the compression block. A Heaviside projection continuation was used to sharpen the density field [4], and a geometric minimum-length constraint enforced a minimum solid feature of 0.55 mm [5]. The finite-element mesh used quadratic tetrahedra in high-gradient regions and linear tetrahedra elsewhere. Three load cases were included for the bracket: vertical pad load, lateral pad load equal to 20% of the vertical load, and bolt-preload-induced bearing pressure. The objective was the weighted compliance over all load cases with local stress used only as a screening metric, not as a formal constraint.

The density field was mapped to two lattice families. Octet-truss cells were selected where the principal stress field was strongly directional, because their stretch-dominated response is efficient when aligned with load paths [10]. Gyroid sheet cells were selected where stress orientation changed rapidly or where fatigue resistance was prioritised, following evidence that triply periodic minimal surface lattices can distribute stress more smoothly than sharp-node trusses [13,14,15]. Unit-cell homogenisation tables were precomputed for relative densities from 8% to 42% and for rotations in 15 degree increments. The mapping followed a dehomogenisation philosophy similar to recent graded-lattice methods [19], but we constrained the final geometry to a finite cell library rather than generating arbitrary microstructure.

Manufacturing constraints and specimen fabrication

All designs were manufactured in AlSi10Mg using laser powder bed fusion on a 400 W class industrial system with 30 micrometre layer thickness. The minimum strut diameter was set to 0.55 mm in the optimiser because preliminary builds showed that nominal 0.40 mm struts were intermittently broken after powder removal. The minimum gyroid wall thickness was set to 0.45 mm. Unsupported downward-facing surfaces were limited to 42 degrees relative to the build plane unless they were shorter than 1.2 mm, reflecting common overhang considerations in additive manufacturing [6,7]. Lattice cavities were required to connect to powder-removal openings with hydraulic diameter above 3.0 mm.

Build orientation was treated as a design variable for the bracket. Five orientations were screened using support volume, predicted overhang violations, estimated recoater collision risk, and alignment between principal struts and the build direction. The final bracket orientation tilted the mounting plane by 18 degrees and the load pad by 11 degrees relative to the build plate. This orientation increased support material by 6% relative to a flat build, but it reduced unsupported lattice members by 28% and improved access for powder evacuation. The optimisation therefore reflects the design-for-AM view that manufacturability is a coupled geometry-process decision [6,8,9].

A total of 42 specimens were printed: 12 compression blocks, 18 bracket specimens, 6 solid tensile coupons, and 6 lattice witness coupons. All parts received stress relief at 300 deg C for 2 h in argon, followed by bead blasting of accessible exterior surfaces. Internal lattice surfaces were left as-built. No hot isostatic pressing was used, because the study aimed to test a realistic low-cost process chain rather than a fully densified aerospace qualification route.

Inspection and mechanical testing

X-ray computed tomography was performed on all compression blocks and on six representative brackets. Voxel size was 18 micrometres for compression blocks and 32 micrometres for brackets. Strut diameters were extracted by skeletonising the segmented lattice and fitting local inscribed cylinders. Node volumes were compared against nominal CAD volumes. Image-based geometric characterisation is increasingly important for additively manufactured lattices because nodes, struts, and thin walls do not deviate uniformly from nominal geometry [18].

Quasi-static compression tests were conducted at 1 mm min^-1 between lubricated platens. Brackets were tested in a custom fixture with bolt preload applied through instrumented washers and load introduced through a hemispherical pad to reduce unintended moment. Displacement was measured by digital image correlation on the bracket sidewall and by actuator displacement corrected for fixture compliance. Fatigue tests used sinusoidal loading at R = 0.1 and 15 Hz, with maximum load set to 55% of the measured mean static peak load for each design family. The fatigue programme was intentionally limited; it was used to compare crack-initiation trends rather than to produce design allowables.

Finite-element models were run at three levels. The first used homogenised continuum properties from the nominal unit-cell library. The second used explicit nominal lattice geometry. The third used CT-corrected strut and wall dimensions for representative specimens. Material properties were taken from printed tensile coupons, which gave Young's modulus of 68.5 +/- 1.9 GPa, 0.2% proof stress of 238 +/- 11 MPa, and ultimate tensile strength of 318 +/- 14 MPa after stress relief.

Results

The graded octet compression blocks showed the highest stiffness at fixed mass, reaching 1.23 +/- 0.05 kN mm^-1 g^-1. Uniform octet blocks reached 1.05 +/- 0.04 kN mm^-1 g^-1, while gyroid blocks reached 0.92 +/- 0.04 kN mm^-1 g^-1. The gyroid blocks, however, failed more gradually and retained 71% of peak load at 8% engineering strain, compared with 48% for the graded octet blocks. This difference reflects the expected trade-off between stretch-dominated truss efficiency and smoother shell-like collapse in TPMS cells [10,11,13].

Bracket tests showed the same pattern at component scale. The optimised graded octet bracket weighed 312 +/- 4 g, 34% less than the stress-screened solid topology-optimised baseline. Its measured initial stiffness was 91% of the solid baseline and 22% higher than a uniform-density octet bracket at the same mass. Peak load was 5.8 +/- 0.3 kN for the graded octet bracket, 6.5 +/- 0.2 kN for the solid topology baseline, and 5.0 +/- 0.4 kN for the uniform lattice. All designs exceeded the 4.2 kN design load, but the failure modes differed. The solid baseline yielded near the bolt fillet, whereas the graded octet design initiated fracture at a lattice-shell transition where local relative density changed abruptly.

The nominal finite-element model over-predicted graded-octet bracket stiffness by 13% and peak load by 16%. CT explained much of the mismatch. Strut diameters in downward-facing members were 6.8% smaller than nominal on average, while node volumes were 11.5% larger than nominal. Missing or partially fused members occurred in 0.7% of inspected octet struts, concentrated near internal corners with poor powder evacuation. Updating the explicit model with CT-corrected strut diameters reduced stiffness error to 5.4% and peak-load error to 8.1%. The remaining mismatch is attributed to surface roughness, residual stress, and local material-property variation not captured in the model.

Fatigue results were more sobering. At the selected load level, gyroid brackets reached runout at 2 x 10^6 cycles in four of six tests, while octet brackets reached runout in two of six. Octet failures initiated at node-strut intersections with visible partially fused particles. Gyroid failures initiated at exterior surface notches near powder-removal openings. The gyroid design had approximately 1.8x longer median crack-initiation life than the octet design at equal mass, but its quasi-static stiffness was 9% lower. A single objective based on static compliance would therefore select the octet design, while a fatigue-sensitive objective would assign more volume to gyroid regions or smooth the octet nodes.

Discussion

The results support topology-optimised lattices as useful structural concepts, but only after manufacturing constraints are made explicit. The largest performance loss did not come from the SIMP optimiser itself. It came from the translation from density field to printable lattice: minimum strut size, cell discretisation, lattice-shell transitions, and powder-removal openings all changed the local load path. This is consistent with prior work arguing that AM constraints must be embedded in the optimisation problem rather than handled as cosmetic post-processing [6,7,8,9].

The comparison between octet and gyroid infill also shows why no single lattice family is universally optimal. The octet truss is efficient for stiffness when members are aligned and when nodes print cleanly [10,12]. The gyroid is less stiff at equal mass in this load case, but it distributes stress more smoothly and reduced fatigue initiation at internal nodes. This agrees with the broader lattice literature: relative density, cell topology, loading mode, print process, and failure criterion interact strongly [13,14,15,16]. A practical optimiser should therefore choose cell families by local function, not by a global preference for one visually appealing lattice.

CT-corrected modelling was crucial. Nominal CAD geometry gave optimistic stiffness and strength predictions, while CT-informed geometry brought simulation and experiment into engineering agreement. The point is not that every production part must be fully scanned; that would be too slow for many applications. Rather, process-characterisation scans should inform design rules for strut compensation, transition smoothing, and minimum drain size. Without that feedback loop, topology optimisation can report false precision.

Several limitations remain. The study used one alloy, one LPBF process window, one heat treatment, and a small fatigue dataset. Surface finishing was minimal, so the fatigue trends should not be treated as final material allowables. Thermal distortion was screened but not coupled into the optimiser. Stress was evaluated after optimisation rather than enforced through a rigorous stress-constrained formulation, and buckling constraints were checked only on the final geometries. The workflow also assumes that the homogenised unit-cell library remains valid near boundaries and lattice-shell transitions, where periodic assumptions are weakest.

Conclusion

We developed and validated a topology-optimisation workflow for additively manufactured lattice structures, combining density-based compliance optimisation, lattice dehomogenisation, AM printability constraints, CT inspection, and mechanical testing. In AlSi10Mg LPBF bracket specimens, graded octet lattices improved stiffness and peak load relative to uniform lattices at equal mass and achieved substantial mass reduction relative to a solid topology-optimised baseline. The numerical benefit was reduced but not erased by manufacturing constraints.

The most important conclusion is that topology optimisation for AM lattices must close the loop between optimiser, unit-cell library, process constraints, and as-built geometry. Designs that look optimal in nominal CAD can fail at lattice-shell transitions or at under-built internal struts. Future work should integrate fatigue and buckling constraints directly into the optimisation, expand the unit-cell library to graded hybrid cells, and use CT-informed process compensation before final design freeze.

Data and code availability

Optimisation meshes, homogenised unit-cell property tables, lattice-mapping scripts, LPBF build files, CT segmentation masks, mechanical-test curves, and post-processing notebooks are included in the supplementary archive. The optimisation scripts were run with MATLAB R2022b and Python 3.10. Finite-element input files are provided in Abaqus format with a README describing material properties, boundary conditions, and fixture-compliance corrections.