Abstract

Additive manufacturing (AM) has been widely adopted to produce mechanical metamaterials for load bearing, energy absorption, and other applications in various industries such as aerospace, automotive, and healthcare. However, geometric imperfections largely exist in AM. Since the mechanical behavior of metamaterials is primarily dependent on their geometries, it is critical to evaluate how process-induced geometric imperfections affect the mechanical behavior of fabricated metamaterials. Most of the existing approaches for AM quality control concentrate on the detection of defects and are limited in their ability to assess defect-altered mechanical behavior of finished builds. Some studies leverage destructive tests or numerical methods for mechanical behavior assessment, which are costly and time-consuming, and impractical for high-throughput routine quality control. In this paper, a new machine learning framework is developed to predict the mechanical behavior of fabricated metamaterials based on their as-built geometries (represented as high-resolution point clouds). Specifically, the point cloud is first converted into an image profile, which preserves detailed geometric patterns. then, a deep neural network is constructed to encode salient features of the image profile and associate them with the load-deflection curve of the fabricated metamaterial. The effectiveness of the developed framework is experimentally validated through a case study with auxetic mechanical metamaterial. This work has great potential to be extended for in-process prediction of AM builds’ mechanical behavior based on layer-wise point cloud scanning.

References

1.
Yu
,
X.
,
Zhou
,
J.
,
Liang
,
H.
,
Jiang
,
Z.
, and
Wu
,
L.
,
2018
, “
Mechanical Metamaterials Associated With Stiffness, Rigidity and Compressibility: A Brief Review
,”
Prog. Mater. Sci.
,
94
, pp.
114
173
.
2.
Surjadi
,
J. U.
,
Gao
,
L.
,
Du
,
H.
,
Li
,
X.
,
Xiong
,
X.
,
Fang
,
N. X.
, and
Lu
,
Y.
,
2019
, “
Mechanical Metamaterials and Their Engineering Applications
,”
Adv. Eng. Mater.
,
21
(
3
), p.
1800864
.
3.
Meeussen
,
A. S.
,
Oğuz
,
E. C.
,
Shokef
,
Y.
, and
Hecke
,
M. V.
,
2020
, “
Topological Defects Produce Exotic Mechanics in Complex Metamaterials
,”
Nat. Phys.
,
16
(
3
), pp.
307
311
.
4.
Askari
,
M.
,
Hutchins
,
D. A.
,
Thomas
,
P. J.
,
Astolfi
,
L.
,
Watson
,
R. L.
,
Abdi
,
M.
,
Ricci
,
M.
, et al
,
2020
, “
Additive Manufacturing of Metamaterials: A Review
,”
Addit. Manuf.
,
36
, p.
101562
.
5.
Yang
,
Y.
,
Liu
,
X.
, and
Kan
,
C.
,
2022
, “
Point Cloud Based Online Detection of Geometric Defects for the Certification of Additively Manufactured Mechanical Metamaterials
,”
J. Manuf. Syst.
,
65
, pp.
591
604
.
6.
Yavari
,
R.
,
Riensche
,
A.
,
Tekerek
,
E.
,
Jacquemetton
,
L.
,
Halliday
,
H.
,
Vandever
,
M.
,
Tenequer
,
A.
, et al
,
2021
, “
Digitally Twinned Additive Manufacturing: Detecting Flaws in Laser Powder Bed Fusion by Combining Thermal Simulations With In-Situ Meltpool Sensor Data
,”
Mater. Des.
,
211
, p.
110167
.
7.
Liu
,
L.
,
Kamm
,
P.
,
García-Moreno
,
F.
,
Banhart
,
J.
, and
Pasini
,
D.
,
2017
, “
Elastic and Failure Response of Imperfect Three-Dimensional Metallic Lattices: The Role of Geometric Defects Induced by Selective Laser Melting
,”
J. Mech. Phys. Solids
,
107
, pp.
160
184
.
8.
Cao
,
X.
,
Jiang
,
Y.
,
Zhao
,
T.
,
Wang
,
P.
,
Wang
,
Y.
,
Chen
,
Z.
,
Li
,
Y.
,
Xiao
,
D.
, and
Fang
,
D.
,
2020
, “
Compression Experiment and Numerical Evaluation on Mechanical Responses of the Lattice Structures With Stochastic Geometric Defects Originated From Additive-Manufacturing
,”
Compos. Part B: Eng.
,
194
, p.
108030
.
9.
Zhang
,
L.
,
Lifton
,
J.
,
Hu
,
Z.
,
Hong
,
R.
, and
Feih
,
S.
,
2022
, “
Influence of Geometric Defects on the Compression Behaviour of Thin Shell Lattices Fabricated by Micro Laser Powder bed Fusion
,”
Addit. Manuf.
,
58
, p.
103038
.
10.
Campoli
,
G.
,
Borleffs
,
M. S.
,
Yavari
,
S. A.
,
Wauthle
,
R.
,
Weinans
,
H.
, and
Zadpoor
,
A. A.
,
2013
, “
Mechanical Properties of Open-Cell Metallic Biomaterials Manufactured Using Additive Manufacturing
,”
Mater. Des.
,
49
, pp.
957
965
.
11.
Yang
,
C.
,
Kim
,
Y.
,
Ryu
,
S.
, and
Gu
,
G. X.
,
2020
, “
Prediction of Composite Microstructure Stress-Strain Curves Using Convolutional Neural Networks
,”
Mater. Des.
,
189
, p.
108509
.
12.
Park
,
D.
,
Jung
,
J.
,
Gu
,
G. X.
, and
Ryu
,
S.
,
2022
, “
A Generalizable and Interpretable Deep Learning Model to Improve the Prediction Accuracy of Strain Fields in Grid Composites
,”
Mater. Des.
,
223
, p.
111192
.
13.
Zhang
,
J.
,
Wang
,
P.
, and
Gao
,
R. X.
,
2019
, “
Deep Learning-Based Tensile Strength Prediction in Fused Deposition Modeling
,”
Comput. Ind.
,
107
, pp.
11
21
.
14.
Xie
,
X.
,
Bennett
,
J.
,
Saha
,
S.
,
Lu
,
Y.
,
Cao
,
J.
,
Liu
,
W. K.
, and
Gan
,
Z.
,
2021
, “
Mechanistic Data-Driven Prediction of As-Built Mechanical Properties in Metal Additive Manufacturing
,”
npj Comput. Mater.
,
7
(
1
), p.
86
.
15.
Seifi
,
S. H.
,
Yadollahi
,
A.
,
Tian
,
W.
,
Doude
,
H.
,
Hammond
,
V. H.
, and
Bian
,
L.
,
2021
, “
In Situ Nondestructive Fatigue-Life Prediction of Additive Manufactured Parts by Establishing a Process–Defect–Property Relationship
,”
Adv. Intell. Syst.
,
3
(
12
), p.
2000268
.
16.
Zhang
,
Z.
,
Liu
,
Q.
, and
Wu
,
D.
,
2022
, “
Predicting Stress–Strain Curves Using Transfer Learning: Knowledge Transfer Across Polymer Composites
,”
Mater. Des.
,
218
, p.
110700
.
17.
Nasiri
,
S.
, and
Khosravani
,
M. R.
,
2021
, “
Machine Learning in Predicting Mechanical Behavior of Additively Manufactured Parts
,”
J. Mater. Res. Technol.
,
14
, pp.
1137
1153
.
18.
Ye
,
Z.
,
Liu
,
C.
,
Tian
,
W.
, and
Kan
,
C.
,
2020
, “
A Deep Learning Approach for the Identification of Small Process Shifts in Additive Manufacturing Using 3D Point Clouds
,”
Proc. Manuf.
,
48
, pp.
770
775
.
19.
Yang
,
Y.
, and
Kan
,
C.
,
2023
, “
Recurrence Network-Based 3D Geometry Representation Learning for Quality Control in Additive Manufacturing of Metamaterials
,”
ASME J. Manuf. Sci. Eng.
,
145
(
11
), p.
111006
.
20.
Aboutaleb
,
A. M.
,
Tschopp
,
M. A.
,
Rao
,
P. K.
, and
Bian
,
L.
,
2017
, “
Multi-Objective Accelerated Process Optimization of Part Geometric Accuracy in Additive Manufacturing
,”
ASME J. Manuf. Sci. Eng.
,
139
(
10
), p.
101001
.
21.
Rao
,
P. K.
,
Kong
,
Z.
,
Duty
,
C. E.
,
Smith
,
R. J.
,
Kunc
,
V.
, and
Love
,
L. J.
,
2015
, “
Assessment of Dimensional Integrity and Spatial Defect Localization in Additive Manufacturing Using Spectral Graph Theory
,”
ASME J. Manuf. Sci. Eng.
,
138
(
5
), p.
051007
.
22.
Jin
,
Y.
,
Qin
,
S. J.
, and
Huang
,
Q.
,
2020
, “
Modeling Inter-Layer Interactions for Out-of-Plane Shape Deviation Reduction in Additive Manufacturing
,”
IISE Trans.
,
52
(
7
), pp.
721
731
.
23.
Scimone
,
R.
,
Taormina
,
T.
,
Colosimo
,
B. M.
,
Grasso
,
M.
,
Menafoglio
,
A.
, and
Secchi
,
P.
,
2022
, “
Statistical Modeling and Monitoring of Geometrical Deviations in Complex Shapes With Application to Additive Manufacturing
,”
Technometrics
,
64
(
4
), pp.
437
456
.
24.
Alghamdi
,
A.
,
Maconachie
,
T.
,
Downing
,
D.
,
Brandt
,
M.
,
Qian
,
M.
, and
Leary
,
M.
,
2020
, “
Effect of Additive Manufactured Lattice Defects on Mechanical Properties: An Automated Method for the Enhancement of Lattice Geometry
,”
Int. J. Adv. Manuf. Technol.
,
108
(
3
), pp.
957
971
.
25.
Samie Tootooni
,
M.
,
Dsouza
,
A.
,
Donovan
,
R.
,
Rao
,
P. K.
,
Kong
,
Z.
, and
Borgesen
,
P.
,
2017
, “
Classifying the Dimensional Variation in Additive Manufactured Parts From Laser-Scanned Three-Dimensional Point Cloud Data Using Machine Learning Approaches
,”
ASME J. Manuf. Sci. Eng.
,
139
(
9
), p.
091005
.
26.
Du
,
J.
,
Yan
,
H.
,
Chang
,
T.-S.
, and
Shi
,
J.
,
2022
, “
A Tensor Voting-Based Surface Anomaly Classification Approach by Using 3D Point Cloud Data
,”
ASME J. Manuf. Sci. Eng.
,
144
(
5
), p.
051005
.
27.
Ye
,
Z.
,
Liu
,
C.
,
Tian
,
W.
, and
Kan
,
C.
,
2021
, “
In-Situ Point Cloud Fusion for Layer-Wise Monitoring of Additive Manufacturing
,”
J. Manuf. Syst.
,
61
, pp.
210
222
.
28.
Liu
,
X.
,
Kan
,
C.
, and
Ye
,
Z.
,
2022
, “
Real-Time Multiscale Prediction of Structural Performance in Material Extrusion Additive Manufacturing
,”
Addit. Manuf.
,
49
, p.
102503
.
29.
Wang
,
R.
,
Law
,
A. C.
,
Garcia
,
D.
,
Yang
,
S.
, and
Kong
,
Z.
,
2021
, “
Development of Structured Light 3D-Scanner With High Spatial Resolution and Its Applications for Additive Manufacturing Quality Assurance
,”
Int. J. Adv. Manuf. Technol.
,
117
, pp.
845
862
.
30.
Liu
,
C.
,
Wang
,
R. R.
,
Ho
,
I.
,
Kong
,
Z. J.
,
Williams
,
C.
,
Babu
,
S.
, and
Joslin
,
C.
,
2022
, “
Toward Online Layer-Wise Surface Morphology Measurement in Additive Manufacturing Using a Deep Learning-Based Approach
,”
J. Intell. Manuf.
,
34
, pp.
2673
2689
.
31.
Lin
,
W.
,
Shen
,
H.
,
Fu
,
J.
, and
Wu
,
S.
,
2019
, “
Online Quality Monitoring in Material Extrusion Additive Manufacturing Processes Based on Laser Scanning Technology
,”
Precis. Eng.
,
60
, pp.
76
84
.
32.
Patané
,
G.
,
2014
, “
Laplacian Spectral Distances and Kernels on 3D Shapes
,”
Pattern Recogn. Lett.
,
47
, pp.
102
110
.
33.
Sun
,
J.
,
Ovsjanikov
,
M.
, and
Guibas
,
L.
,
2009
, “
A Concise and Provably Informative Multi-scale Signature Based on Heat Diffusion
,”
Comput. Graph. Forum
,
28
(
5
), pp.
1383
1392
.
34.
Fang
,
Y.
,
Xie
,
J.
,
Dai
,
G.
,
Wang
,
M.
,
Zhu
,
F.
,
Xu
,
T.
, and
Wong
,
E.
,
2015
, “
3D Deep Shape Descriptor
,”
Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition
,
Boston, MA
,
June 7–12
, pp.
2319
2328
.
35.
Li
,
C.
, and
Ben Hamza
,
A.
,
2013
, “
A Multiresolution Descriptor for Deformable 3D Shape Retrieval
,”
Visual Comput.
,
29
(
6–8
), pp.
513
524
.
36.
Xu
,
G.
,
2004
, “
Convergence of Discrete Laplace-Beltrami Operators Over Surfaces
,”
Comput. Math. Appl.
,
48
(
3–4
), pp.
347
360
.
37.
Xie
,
J.
,
Dai
,
G.
,
Zhu
,
F.
,
Wong
,
E. K.
, and
Fang
,
Y.
,
2016
, “
Deepshape: Deep-Learned Shape Descriptor for 3D Shape Retrieval
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
39
(
7
), pp.
1335
1345
.
38.
Hinton
,
G. E.
, and
Salakhutdinov
,
R. R.
,
2006
, “
Reducing the Dimensionality of Data With Neural Networks
,”
Science
,
313
(
5786
), pp.
504
507
.
39.
Sergin
,
N. D.
, and
Yan
,
H.
,
2021
, “
Toward a Better Monitoring Statistic for Profile Monitoring Via Variational Autoencoders
,”
J. Qual. Technol.
,
53
(
5
), pp.
454
473
.
40.
Li
,
L.
,
Yan
,
J.
,
Wang
,
H.
, and
Jin
,
Y.
,
2020
, “
Anomaly Detection of Time Series With Smoothness-Inducing Sequential Variational Auto-Encoder
,”
IEEE Trans. Neural Netw. Learn. Syst.
,
32
(
3
), pp.
1177
1191
.
41.
Kingma
,
D. P.
, and
Welling
,
M.
,
2014
, “
Autoencoding Variational Bayes
,”
Presented at the 2nd International Conference on Learning Representations
,
Banff, Canada
,
Apr. 14–16
.
42.
Joo
,
S.
,
Jung
,
W.
, and
Oh
,
S. E.
,
2023
, “
Variational Autoencoder-Based Estimation of Chronological Age and Changes in Morphological Features of Teeth
,”
Sci. Rep.
,
13
(
1
), p.
704
.
43.
Zhao
,
Q.
,
Adeli
,
E.
,
Honnorat
,
N.
,
Leng
,
T.
, and
Pohl
,
K. M.
,
2019
, “
Variational Autoencoder for Regression: Application to Brain Aging Analysis
,”
International Conference on Medical Image Computing and Computer-Assisted Intervention
,
Shenzhen, China
,
Springer
, pp.
823
831
.
44.
Wang
,
H.
,
Zhang
,
Y.
,
Lin
,
W.
, and
Qin
,
Q.-H.
,
2020
, “
A Novel Two-Dimensional Mechanical Metamaterial With Negative Poisson’s Ratio
,”
Comput. Mater. Sci.
,
171
, p.
109232
.
45.
Ren
,
X.
,
Das
,
R.
,
Tran
,
P.
,
Ngo
,
T. D.
, and
Xie
,
Y. M.
,
2018
, “
Auxetic Metamaterials and Structures: A Review
,”
Smart Mater. Struct.
,
27
(
2
), p.
023001
.
46.
Zhang
,
G.
, and
Khandelwal
,
K.
,
2019
, “
Computational Design of Finite Strain Auxetic Metamaterials Via Topology Optimization and Nonlinear Homogenization
,”
Comput. Meth. Appl. Mech. Eng.
,
356
, pp.
490
527
.
47.
Bazant
,
Z. P.
,
2010
, “
Can Multiscale-Multiphysics Methods Predict Softening Damage and Structural Failure?
,”
Int. J. Multiscale Comput. Eng.
,
8
(
1
), pp.
61
67
.
48.
Yan
,
H.
,
Paynabar
,
K.
, and
Pacella
,
M.
,
2019
, “
Structured Point Cloud Data Analysis Via Regularized Tensor Regression for Process Modeling and Optimization
,”
Technometrics
,
61
(
3
), pp.
385
395
.
49.
Pasini
,
D.
, and
Guest
,
J. K.
,
2019
, “
Imperfect Architected Materials: Mechanics and Topology Optimization
,”
MRS Bull.
,
44
(
10
), pp.
766
772
.
50.
Tancogne-Dejean
,
T.
,
Roth
,
C. C.
,
Woy
,
U.
, and
Mohr
,
D.
,
2016
, “
Probabilistic Fracture of Ti–6Al–4 V Made Through Additive Layer Manufacturing
,”
Int. J. Plast.
,
78
, pp.
145
172
.
51.
Pathan
,
M. V.
,
Ponnusami
,
S. A.
,
Pathan
,
J.
,
Pitisongsawat
,
R.
,
Erice
,
B.
,
Petrinic
,
N.
, and
Tagarielli
,
V. L.
,
2019
, “
Predictions of the Mechanical Properties of Unidirectional Fibre Composites by Supervised Machine Learning
,”
Sci. Rep.
,
9
(
1
), pp.
1
10
.
52.
Wang
,
L.
,
Chan
,
Y.-C.
,
Ahmed
,
F.
,
Liu
,
Z.
,
Zhu
,
P.
, and
Chen
,
W.
,
2020
, “
Deep Generative Modeling for Mechanistic-Based Learning and Design of Metamaterial Systems
,”
Comput. Meth. Appl. Mech. Eng.
,
372
, p.
113377
.
53.
Maggipinto
,
M.
,
Beghi
,
A.
,
McLoone
,
S.
, and
Susto
,
G. A.
,
2019
, “
DeepVM: A Deep Learning-Based Approach With Automatic Feature Extraction for 2D Input Data Virtual Metrology
,”
J. Process Control
,
84
, pp.
24
34
.
54.
Yang
,
H.
,
Kan
,
C.
,
Liu
,
G.
, and
Chen
,
Y.
,
2013
, “
Spatiotemporal Differentiation of Myocardial Infarctions
,”
IEEE Trans. Autom. Sci. Eng.
,
10
(
4
), pp.
938
947
.
55.
Wang
,
Y.
,
Sun
,
W.
,
Jin
,
J.
,
Kong
,
Z.
, and
Yue
,
X.
,
2023
, “
MVGCN: Multi-view Graph Convolutional Neural Network for Surface Defect Identification Using Three-Dimensional Point Cloud
,”
ASME J. Manuf. Sci. Eng.
,
145
(
3
), p.
031004
.
56.
Zhang
,
Y.
,
Yang
,
S.
,
Dong
,
G.
, and
Zhao
,
Y. F.
,
2021
, “
Predictive Manufacturability Assessment System for Laser Powder Bed Fusion Based on a Hybrid Machine Learning Model
,”
Addit. Manuf.
,
41
, p.
101946
.
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