Abstract

Additive manufacturing (AM) has enabled the production of intricate lattice structures with excellent performance and minimal mass. Design approaches that consider static loading, including lattice-based topology optimization (TO), have been well-researched recently. However, to date, there appears to be no widely accepted method of optimizing lattice structures for high-strain rate loading, especially when the design for additive manufacturing (DFAM) principles are considered. This study proposes a computational framework for the design of lattice structures under specified impact loading. To manage dimensionality while achieving sufficient generality, a heuristic design space is developed that relies on traditional TO to govern the design's macrostructure and standard dimensioning to govern its mesostructure. DFAM principles are then incorporated into a Bayesian optimization scheme wrapped around traditional TO to achieve manufacturable designs that absorb high-impact loading. Because this approach does not require analytical gradient information, the framework can be used to optimize directly on complex objectives, such as injury metrics calculated from the acceleration curve. A series of case studies is formulated around a mass-performance tradeoff and involves individual unit cell design as well as full-part design. The proposed design parameterization is found to enable sufficient flexibility to achieve consistently good performance regardless of AM build orientation.

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References

1.
Zhang
,
B.
,
Goel
,
A.
, and
Ghalsasi
,
O.
,
2019
, “
CAD-Based Design and Pre-Processing Tools for Additive Manufacturing
,”
J. Manuf. Syst.
,
52
(
B
), pp.
227
241
.
2.
Bendsøe
,
M. P.
, and
Kikuchi
,
N.
,
1988
, “
Generating Optimal Topologies in Structural Design Using a Homogenization Method
,”
Comput. Methods Appl. Mech. Eng.
,
71
(
2
), pp.
197
224
.
3.
Bendsøe
,
M.
,
1989
, “
Optimal Shape Design as a Material Distribution Problem
,”
Struct. Optim.
,
1
(
4
), pp.
193
202
.
4.
Ranjan
,
R.
,
Samant
,
R.
, and
Anand
,
S.
,
2017
, “
Integration of Design for Manufacturing Methods With Topology Optimization in Additive Manufacturing
,”
ASME J. Manuf. Sci. Eng.
,
139
(
6
), p.
061007
.
5.
Langelaar
,
M.
,
2017
, “
An Additive Manufacturing Filter for Topology Optimization of Print-Ready Designs
,”
Struct. Multidiscipl. Optim.
,
55
(
3
), pp.
871
883
.
6.
Langelaar
,
M.
,
2016
, “
Topology Optimization for Additive Manufacturing with Controllable Support Structure Costs
,”
Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering, National Technical University of Athens (NTUA)
,
Crete Island, Greece
,
June 5–10
.
7.
McConaha
,
M.
,
Venugopal
,
V.
, and
Anand
,
S.
,
2020
, “
Integration of Machine Tool Accessibility of Support Structures With Topology Optimization for Additive Manufacturing
,”
Proceedings of the North American Manufacturing Research Conference
,
Virtual, Online
,
June
, pp.
634
642
.
8.
Mhapsekar
,
K.
,
McConaha
,
M.
, and
Anand
,
S.
,
2018
, “
Additive Manufacturing Constraints in Topology Optimization for Improved Manufacturability
,”
ASME J. Manuf. Sci. Eng.
,
140
(
5
), p.
051017
.
9.
Maskery
,
I.
,
Sturm
,
L.
,
Aremu
,
A. O.
,
Panesar
,
A.
,
Williams
,
C. B.
,
Tuck
,
C. J.
,
Wildman
,
R. D.
,
Ashcroft
,
I. A.
, and
Hague
,
R. J.
,
2018
, “
Insights Into the Mechanical Properties of Several Triply Periodic Minimal Surface Lattice Structures Made by Polymer Additive Manufacturing
,”
Polymer
,
152
, pp.
62
71
.
10.
Wauthle
,
R.
,
Vrancken
,
B.
, and
Beynaerts
,
B.
,
2015
, “
Effects of Build Orientation and Heat Treatment on the Microstructure and Mechanical Properties of Selective Laser Melted Ti6Al4V Lattice Structures
,”
Addit. Manuf.
,
5
, pp.
77
84
.
11.
Park
,
S.
,
Rosen
,
D. W.
, and
Choi
,
S.
,
2014
, “
Effective Mechanical Properties of Lattice Material Fabricated by Material Extrusion Additive Manufacturing
,”
Addit. Manuf.
,
1–4
, pp.
12
23
.
12.
Gümrük
,
R.
,
Mines
,
R. A. W.
, and
Karadeniz
,
S.
,
2018
, “
Determination of Strain Rate Sensitivity of Micro-Struts Manufactured Using the Selective Laser Melting Method
,”
J. Mater. Eng. Perform.
,
27
(
3
), pp.
1016
1032
.
13.
Liu
,
C.
,
Du
,
Z.
, and
Zhang
,
W.
,
2017
, “
Additive Manufacturing-Oriented Design of Graded Lattice Structures Through Explicit Topology Optimization
,”
ASME J. Appl. Mech.
,
84
(
8
), p.
081008
.
14.
Zhang
,
B.
,
Mhapsekar
,
K.
, and
Anand
,
S.
,
2017
, “
Design of Variable-Density Structures for Additive Manufacturing Using Gyroid Lattices
,”
Proceedings of the International Design Engineering Technical Conference
,
Cleveland, OH
,
August 2017
.
15.
McConaha
,
M.
,
2018
, “
Graded Lattice Structure Density Optimization for Additive Manufacturing
,”
MS thesis
,
University of Cincinnati
,
Cincinnati, OH
.
16.
Liu
,
Y.
,
2008
, “
Optimum Design of Straight Thin-Walled Box Section Beams for Crashworthiness Analysis
,”
Finite Elem. Anal. Des.
,
44
(
3
), pp.
139
147
.
17.
Reinhart
,
G.
, and
Teufelhart
,
S.
,
2013
, “
Optimization of Mechanical Loaded Lattice Structures by Orientating Their Struts Along the Flux of Force
,”
Procedia CIRP
,
12
, pp.
175
180
.
18.
Levadnyi
,
I.
,
Awrejcewicz
,
J.
, and
Zhang
,
Y.
,
2018
, “
Finite Element Analysis of Impact for Helmeted and Non-Helmeted Head
,”
J. Med. Biol. Eng.
,
38
(
4
), pp.
587
595
.
19.
Szczyrba
,
I.
,
Burtscher
,
M.
, and
Szczyrba
,
R.
,
2012
, “
Validating Critical Limits of the Universal Brain Injury Criterion
,”
Proceedings of the International Conference on Bioinformatics & Computational Biology
,
Orlando, FL
,
Oct. 7–10
, p.
134
.
20.
Takhounts
,
E. G.
,
Craig
,
M. J.
, and
Moorhouse
,
K.
,
2013
, “
Development of Brain Injury Criteria (BrIC)
,”
Stapp Car Crash J.
,
57
, pp.
243
266
.
21.
U.S. Department of Transportation
,
2016
, “Laboratory Test Procedure for FMVSS No. 201U: Occupant Protection in Interior Impact,” TP-201U-02, Washington, DC.
22.
Lee
,
H.
, and
Park
,
G.
,
2012
, “
Topology Optimization for Structures With Nonlinear Behavior Using the Equivalent Static Loads Method
,”
ASME J. Mech. Des.
,
134
(
3
), p.
031004
.
23.
Chuang
,
C. H.
, and
Yang
,
R. J.
,
2012
, “
Benchmark of Topology Optimization Methods for Crashworthiness Design
,”
Proceedings of the 12th International LS-DYNA Users Conference
,
Detroit, MI
,
June 3–5
.
24.
Duddeck
,
F.
,
2012
, “
A New Topology Optimization Approach for Crashworthiness of Passenger Vehicles Based on Physically Defined Equivalent Static Loads
,”
Proceedings of the International Crash Worthiness Conference
,
Milan, Italy
,
July 2021
, pp.
1
13
.
25.
Patel
,
N. M.
,
Kang
,
B.
, and
Renaud
,
J. E.
,
2008
, “
Crashworthiness Design Using a Hybrid Cellular Automaton Algorithm
,”
Proceedings of the International Design Engineering Technical Conference
,
Philadelphia, PA
,
July
, pp.
151
162
.
26.
Bandi
,
P.
,
Mozumder
,
C.
, and
Tovar
,
A.
,
2010
, “
Crashworthiness Design for Multiple Loading Conditions Using Dynamic Weighting Factors in HCA Framework
,”
Proceedings of the AIAA/ISSMO Multidisciplinary Analysis Optimization Conference
,
Fort Worth, TX
,
Sept. 13–15
.
27.
Hertlein
,
N.
,
Vemaganti
,
K.
, and
Anand
,
S.
, “
Bayesian Optimization of Energy-Absorbing Lattice Structures for Additive Manufacturing
,”
Proceedings of the ASME IMECE Conference. Virtual, Online
,
Virtual, Online
,
Nov. 16–19
.
28.
Schultz
,
J.
,
Griese
,
D.
,
Ju
,
J.
,
2012
, “
Design of Honeycomb Mesostructures for Crushing Energy Absorption
,”
ASME J. Mech. Des.
,
134
(
7
), p.
071004
.
29.
Liu
,
K.
,
Detwiler
,
D.
, and
Tovar
,
A.
,
2018
, “
Cluster-Based Optimization of Cellular Materials and Structures for Crashworthiness
,”
ASME J. Mech. Des.
,
140
(
11
), p.
111412
.
30.
Fang
,
J.
,
Sun
,
G.
, and
Qiu
,
N.
,
2017
, “
On Design Optimization for Structural Crashworthiness and Its State of the Art
,”
Struct. Multidiscipl. Optim.
,
55
(
3
), pp.
1091
1119
.
31.
Andreassen
,
E.
,
Clausen
,
A.
, and
Schevenels
,
M.
,
2011
, “
Efficient Topology Optimization in MATLAB Using 88 Lines of Code
,”
Struct. Multidiscipl. Optim.
,
43
(
1
), pp.
1
16
.
32.
Kawamura
,
H.
,
Ohmori
,
H.
, and
Kito
,
N.
,
2002
, “
Truss Topology Optimization by a Modified Genetic Algorithm
,”
Struct. Multidiscipl. Optim.
,
23
(
6
), pp.
467
473
.
33.
Luh
,
G.
,
Lin
,
C.
, and
Lin
,
Y.
,
2011
, “
A Binary Particle Swarm Optimization for Continuum Structural Topology Optimization
,”
Appl. Soft Comput.
,
11
(
2
), pp.
2833
2844
.
34.
Liu
,
Y.
,
Dong
,
Z.
, and
Ge
,
J.
,
2019
, “
Stiffness Design of a Multilayer Arbitrary BCC Lattice Structure With Face Sheets
,”
Compos. Struct.
,
230
, p.
111485
.
35.
Hanks
,
B.
, and
Frecker
,
M.
,
2019
, “
Lattice Structure Design for Additive Manufacturing: Unit Cell Topology Optimization
,”
Proceedings of the International Design Engineering Technical Conference
,
Anaheim, CA
,
August 2019
.
36.
Li
,
D.
,
Liao
,
W.
, and
Dai
,
N.
,
2020
, “
Anisotropic Design and Optimization of Conformal Gradient Lattice Structures
,”
Comput.-Aided Des.
,
119
.
37.
Forsberg
,
J.
, and
Nilsson
,
L.
,
2007
, “
Topology Optimization in Crashworthiness Design
,”
Struct. Multidiscipl. Optim.
,
33
(
1
), pp.
1
12
.
38.
Hutchinson
,
J.
,
Kaiser
,
M. J.
, and
Lankarani
,
H. M.
,
1998
, “
The Head Injury Criterion (HIC) Functional
,”
Appl. Math. Comput.
,
96
(
1
), pp.
1
16
.
39.
Yoo
,
D.
,
Hertlein
,
N.
, and
Chen
,
V.
,
2021
, “
Bayesian Optimization of Equilibrium States in Elastomeric Beams
,”
ASME J. Mech. Des.
,
143
(
11
), p.
111702
.
40.
Lam
,
R.
,
Poloczek
,
M.
, and
Frazier
,
P.
,
2018
, “
Advances in Bayesian Optimization With Applications in Aerospace Engineering
,”
Proceedings of the AIAA Non-Deterministic Approaches Conference
,
Kissimmee, FL
,
January 2018
.
41.
Rasmussen
,
C.
, and
Williams
,
C.
,
2006
,
Gaussian Processes for Machine Learning
,
MIT Press
,
Cambridge, MA
.
42.
Couckuyt
,
I.
,
Deschrijver
,
D.
, and
Dhaene
,
T.
,
2014
, “
Fast Calculation of Multiobjective Probability of Improvement and Expected Improvement Criteria for Pareto Optimization
,”
J. Global Optim.
,
60
(
3
), pp.
575
594
.
43.
Majeed
,
A.
,
Ahmed
,
A.
, and
Liu
,
B.
,
2019
, “
Influence of Wall Thickness on the Hardness of AlSi10Mg Alloy Parts Manufactured by Selective Laser Melting
,”
Procedia CIRP
,
81
, pp.
459
463
.
44.
Gardner
,
J.
,
Kusner
,
M.
, and
Weinberger
,
K.
,
2014
, “
Bayesian Optimization With Inequality Constraints
,”
Proceedings of the 31st International Conference on Machine Learning
,
Beijing, China
,
June
, pp.
937
945
.
45.
Knudde
,
N.
,
van der Herten
,
J.
, and
Dhaene
,
T.
,
2017
, “
GPFlowOpt: A Bayesian Optimization Library Using TensorFlow
,”
arXiv preprint
. https://arxiv.org/abs/1711.03845
46.
Mines
,
R. A. W.
,
Tsopanos
,
S.
, and
McKown
,
S. T.
,
2011
, “
Verification of a Finite Element Simulation of the Progressive Collapse of Micro Lattice Structures
,”
Appl. Mech. Mater.
,
70
, pp.
111
116
.
47.
Livermore Software Technology Corporation
. “LS-DYNA Keyword User's Manual Volume II: Material Models.” http://www.lstc.com/download/manuals, Accessed April 2020.
48.
Hernandez
,
C.
,
Maranon
,
A.
, and
Ashcroft
,
I. A.
,
2013
, “
A Computational Determination of the Cowper–Symonds Parameters From a Single Taylor Test
,”
Appl. Math. Model.
,
37
(
7
), pp.
4698
4708
.
49.
Chang
,
J. M.
,
Tyan
,
T.
, and
El-bkaily
,
M.
,
2007
, “
Implicit and Explicit Finite Element Methods for Crash Safety Analysis
,”
SAE Trans.
,
116
(
6
), pp.
1025
1037
.
50.
Livermore Software Technology
, “LS-DYNA,” R10.1.0. www.lstc.com.
51.
Smith
,
M.
,
Guan
,
Z.
, and
Cantwell
,
W. J.
,
2013
, “
Finite Element Modelling of the Compressive Response of Lattice Structures Manufactured Using the Selective Laser Melting Technique
,”
Int. J. Mech. Sci.
,
67
, pp.
28
41
.
52.
Livermore Software Technology Corporation
. “LS-DYNA Theory Manual,” http://www.lstc.com/download/manuals, Accessed July 2021.
53.
Nassar
,
A. R.
, and
Reutzel
,
E. W.
,
2015
, “
Beyond Layer-by-Layer Additive Manufacturing – Voxel-Wise Directed Energy Deposition
,”
Solid Freeform Fabrication Symposium
,
Austin, TX
,
Aug. 10–12
, pp.
273
283
.
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