Abstract
Ever since its introduction over five decades ago, geometric solid modeling has been crucial for engineering design purposes and is used in engineering software packages such as computer-aided design (cad), computer-aided manufacturing, computer-aided engineering, etc. Solid models produced by cad software have been used to transfer geometric information from designers to manufacturers. Since the emergence of additive manufacturing (AM), a CAD file can also be directly uploaded to a three-dimensional (3D) printer and used for production. AM techniques allow manufacturing of complex geometric objects such as bio-inspired structures and lattice structures. These structures are shapes inspired by nature and periodical geometric shapes consisting of struts interconnecting in nodes. Both structures have unique properties such as significantly reduced weight. However, geometric modeling of such structures has significant challenges due to the inability of current techniques to handle their geometric complexity. This calls for a novel modeling method that would allow engineers to design complex geometric objects. This survey paper reviews geometric modeling methods of complex structures to support bio-inspired design created for AM which includes discussing reasoning behind bio-inspired design, limitations of current modeling approaches applied to bio-inspired structures, challenges encountered with geometric modeling, and opportunities that these challenges reveal. Based on the review, a need for a novel geometric modeling method for bio-inspired geometries produced by AM is identified. A framework for such a bio-inspired geometric modeling method is proposed as a part of this work.
References
1.
Li
, S.
, Bai
, H.
, Shepherd
, R. F.
, and Zhao
, H.
, 2019
, “Bio-Inspired Design and Additive Manufacturing of Soft Materials, Machines, Robots, and Haptic Interfaces
,” Angew. Chem. Int. Ed.
, 58
(33
), pp. 11182
–11204
. 2.
Dmitry
, B.
, 2016
, “Evening Light, Kiyomizu-Dera Temple, Kyoto
,” https://www.flickr.com/photos/ru_boff/317341034463.
Weiskittel
, A. R.
, Kershaw
, J. A.
, Hofmeyer
, P. V.
, and Seymour
, R. S.
, 2009
, “Species Differences in Total and Vertical Distribution of Branch- and Tree-Level Leaf Area for the Five Primary Conifer Species in Maine, USA
,” For. Ecol. Manage.
, 258
(7
), pp. 1695
–1703
. 4.
Fazio
, M. W.
, Moffett
, M.
, and Wodehouse
, L.
, 2013
, A World History of Architecture
, 3rd ed., Laurence King
, London
.5.
Lutfi
, M.
, 2018
, “The Effect of Gravitational Field on Brachistochrone Problem
,” J. Phys. Conf. Ser.
, 1028
, p. 012060
. 6.
Ashby
, N.
, Brittin
, W. E.
, Love
, W. F.
, and Wyss
, W.
, 1975
, “Brachistochrone With Coulomb Friction
,” Am. J. Phys.
, 43
(10
), pp. 902
–906
. 7.
Monn
, M. A.
, 2017
, “Learning New Tricks from Sea Sponges, Nature’s Most Unlikely Civil Engineers
,” The Conversation, https://theconversation.com/learning-new-tricks-from-sea-sponges-natures-most-unlikely-civil-engineers-803738.
Li
, L.
, Guo
, C.
, Chen
, Y.
, and Chen
, Y.
, 2020
, “Optimization Design of Lightweight Structure Inspired by Glass Sponges (Porifera, Hexacinellida) and Its Mechanical Properties
,” Bioinspir. Biomim.
, 15
(3
), p. 036006
. 9.
Rayker
, K.
, 2008
, Honeycomb (CC BY 2.0), https://www.flickr.com/photos/krayker/2268587409
10.
Redback Aviation
, 2017
, “Understanding Rotor Blades—The Rotary Wing
,” Redback Aviation, http://www.redbackaviation.com/understanding-rotor-blades-the-rotary-wing/11.
Bar-Cohen
, Y.
, 2005
, Biomimetics. Biologically Inspired Technologies
, 1st ed., CRC Press
, Boca Raton, FL
.12.
Kerrick
, D.
, 2011
, “From Wood to Composite Materials The Evolution of the Rotor Blade
,” Helicopter Maintenance Magazine
, https://helicoptermaintenancemagazine.com/article/wood-composite-materials-evolution-rotor-blade13.
ASTM
, 2015
, ASTM F2792-12a: Standard Terminology for Additive Manufacturing Technologies
, ASTM International
, West Conshohocken, PA
.14.
Dassault Systèmes SE
, 2020
, “SOLIDWORKS and SW Data Management System Requirements
,” SOLIDWORKS, https://www.solidworks.com/sw/support/SystemRequirements.html15.
Robert McNeel & Associates
, 2020
, “System Requirements
,” Rhino System Requirements, https://www.rhino3d.com/6/system_requirements16.
Kamaci
, N.
, and Altunbasak
, Y.
, 2003
, “Performance Comparison of the Emerging H.264 Video Coding Standard With the Existing Standards
,” Proceedings of the 2003 International Conference on Multimedia and Expo. ICME’03
, IEEE
, pp. I
–345
, Cat. No. 03TH8698.17.
Kianian
, B.
, 2017
, “Wohlers Report 2017: 3D Printing and Additive Manufacturing State of the Industry, Annual Worldwide Progress Report
,” 22nd ed. Wohlers Associates, Inc.
18.
Attene
, M.
, 2018
, “As-Exact-as-Possible Repair of Unprintable STL Files
,” Rapid Prototyp. J.
, 24
(5
), pp. 855
–864
. 19.
Wohlers
, T. T.
, and Gornet
, T.
, 2014
, “History of Additive Manufacturing
,” Wohlers Rep.
, 24
(2014
), p. 118
.20.
Taufik
, M.
, and Jain
, P.
, 2016
, “Additive Manufacturing: Current Scenario
,” International Conference on Advanced Production and Industrial Engineering, ICAPIE 2016
, New Delhi, India
, Dec. 10
, pp. 380
–386
.21.
Hamelin
, R. D.
, Walden
, D. D.
, and Krueger
, M. E.
, 2010
, “4.4.2 INCOSE Systems Engineering Handbook v3.2: Improving the Process for SE Practitioners
,” INCOSE Int. Symp.
, 20
(1
), pp. 532
–541
. 22.
Edalat
, A.
, and Lieutier
, A.
, 2002
, “Foundation of a Computable Solid Modelling
,” Theor. Comput. Sci.
, 284
(2
), pp. 319
–345
. 23.
Kou
, X. Y.
, and Tan
, S. T.
, 2007
, “Heterogeneous Object Modeling: A Review
,” Comput. Aided Des.
, 39
(4
), pp. 284
–301
. 24.
Rosen
, D. W.
, 2007
, “Computer-Aided Design for Additive Manufacturing of Cellular Structures
,” Comput. Aided Des.
, 4
(5
), pp. 585
–594
. 25.
Dimas
, L. S.
, and Buehler
, M. J.
, 2014
, “Modeling and Additive Manufacturing of Bio-Inspired Composites With Tunable Fracture Mechanical Properties
,” Soft Matter
, 10
(25
), p. 4436
. 26.
Panda
, B. N.
, 2015
, “Design and Development of Cellular Structure for Additive Manufacturing
,” Ph.D. thesis
, National Institute of Technology Rourkela
, Rourkela, India
.27.
Tang
, Y.
, and Zhao
, Y. F.
, 2016
, “A Survey of the Design Methods for Additive Manufacturing to Improve Functional Performance
,” Rapid Prototyp. J.
, 22
(3
), pp. 569
–590
. 28.
C3D Labs
, 2016
, “C3D Toolkit. Developer Manual
,” https://c3dlabs.com/source/pdf/c3d/2016-C3D_Manual_English.pdf29.
Gu
, G. X.
, Su
, I.
, Sharma
, S.
, Voros
, J. L.
, Qin
, Z.
, and Buehler
, M. J.
, 2016
, “Three-Dimensional-Printing of Bio-Inspired Composites
,” ASME J. Biomech. Eng.
, 138
(2
), p. 021006
. 30.
Savio
, G.
, Rosso
, S.
, Meneghello
, R.
, and Concheri
, G.
, 2018
, “Geometric Modeling of Cellular Materials for Additive Manufacturing in Biomedical Field: A Review
,” Appl. Bionics Biomech.
, 2018
, pp. 1654782:1
–1654782:14
. 31.
Golovanov
, N.
, 2014
, Geometric Modeling
, CreateSpace Independent Publishing Platform
, Scotts Valley, CA
.32.
Gardan
, Y.
, 1985
, Mathematics and CAD: Numerical Methods for CAD
, The MIT Press
, Cambridge, MA
.33.
Ushakov
, D. M.
, 2018
, Introduction to the Mathematical Foundations of CAD
, 2nd ed., DMK Press
, Moscow, Russia
.34.
Ushakov
, D. M.
, 2012
, “Russian National 3D Kernel
,” Isicad, http://isicad.net/articles.php?article_num=1518935.
Schnitger Corporation
, 2012
, New Math. The Hidden Cost of Swapping CAD Kernels
, Schnitger Corporation
, https://schnitgercorp.com/wp-content/uploads/2020/12/SchnitgerCorp-Hidden-Cost-of-Kernel-Change-2020.pdf36.
Friedenthal
, S.
, Moore
, A.
, and Steiner
, R.
, 2015
, A Practical Guide to SysML
, 3rd ed., S.
Elliot
, ed., Elsevier
, Waltham, MA
, pp. 417
–504
.37.
Hosaka
, M.
, 2012
, Modeling of Curves and Surfaces in CAD/CAM
, Springer Science and Business Media
, Berlin, Germany
.38.
Pasko
, A.
, Adzhiev
, V.
, Sourin
, A.
, and Savchenko
, V.
, 1995
, “Function Representation in Geometric Modeling: Concepts, Implementation and Applications
,” Vis. Comput.
, 11
(8
), pp. 429
–446
. 39.
Hatcher
, A.
, 2002
, Algebraic Topology
, No eBook available Cambridge University Press
, Cambridge
.40.
Letov
, N.
, and Zhao
, Y. F.
, 2020
, “Volumetric Cells: A Framework for a Bio-Inspired Geometric Modelling Method to Support Heterogeneous Lattice Structures
,” Proceedings of the Design Society: DESIGN Conference
, Dubrovnik, Croatia
, May 1
, pp. 295
–304
.41.
Braun
, P.
, Sliwinski
, M.
, Hinckeldeyn
, J.
, and Kreutzfeldt
, J.
, 2021
, “Challenges of CAD Conversion to 3D Development Environments With Respect to Kinematic Dependencies
,” Proceedings of SIMS 2020
, Virtual, Finland
, Sept. 22–24
, pp. 215
–221
.42.
43.
Cutanda
, V.
, Juhl
, P. M.
, and Jacobsen
, F.
, 2001
, “On the Modeling of Narrow Gaps Using the Standard Boundary Element Method
,” J. Acoust. Soc. Am.
, 109
(4
), pp. 1296
–1303
. 44.
Enterfea
, 2017
, “Correct Mesh Size—A Quick Guide
,” https://enterfea.com/correct-mesh-size-quick-guide/45.
Gillebaart
, T.
, van Zuijlen
, A.
, and Bijl
, H.
, 2016
, “Radial Basis Function Mesh Deformation Including Surface Orthogonality
,” 54th AIAA Aerospace Sciences Meeting
, Reston, VA
, Jan. 4–8
, pp. 1
–7
.46.
Kedward
, L.
, Allen
, C. B.
, and Rendall
, T.
, 2017
, “Efficient and Exact Mesh Deformation Using Multi-Scale RBF Interpolation
,” 55th AIAA Aerospace Sciences Meeting
, Grapevine, TX
, Jan. 9–13
, pp. 1
–19
.47.
Zhao
, Z.
, Ma
, R.
, He
, L.
, Chang
, X.
, and Zhang
, L.
, 2020
, “An Efficient Large-Scale Mesh Deformation Method Based on MPI/OpenMP Hybrid Parallel Radial Basis Function Interpolation
,” Chin. J. Aeronaut.
, 33
(5
), pp. 1392
–1404
. 48.
Stroud
, I.
, 2006
, Boundary Representation Modelling Techniques
, Springer Nature
, London, UK
.49.
Sánchez-Reyes
, J.
, 1995
, “Quasinonparametric Surfaces
,” Comput. Aided Des.
, 27
(4
), pp. 263
–275
. 50.
Song
, Y.
, and Cohen
, E.
, 2019
, “Refinement for a Hybrid Boundary Representation and Its Hybrid Volume Completion
,” SMAI J. Comput. Math.
, S5
, pp. 3
–25
. 51.
Wang
, X.
, and Qian
, X.
, 2014
, “An Optimization Approach for Constructing Trivariate B-Spline Solids
,” Comput. Aided Des.
, 46
, pp. 179
–191
. 52.
Sasaki
, Y.
, Takezawa
, M.
, Kim
, S.
, Kawaharada
, H.
, and Maekawa
, T.
, 2017
, “Adaptive Direct Slicing of Volumetric Attribute Data Represented by Trivariate B-Spline Functions
,” Int. J. Adv. Manuf. Technol.
, 91
(5–8
), pp. 1791
–1807
. 53.
Rogers
, D. F.
, 2001
, An Introduction to NURBS: With Historical Perspective
, Morgan Kaufmann
, Burlington, MA
.54.
Schmidt
, R.
, Wüchner
, R.
, and Bletzinger
, K.-U.
, 2012
, “Isogeometric Analysis of Trimmed NURBS Geometries
,” Comput. Methods Appl. Mech. Eng.
, 241–244
, pp. 93
–111
. 55.
Boender
, E.
, Bronsvoort
, W. F.
, and Post
, F. H.
, 1994
, “Finite-Element Mesh Generation From Constructive-Solid-Geometry Models
,” Comput. Aided Des.
, 26
(5
), pp. 379
–392
. 56.
Joan-Arinyo
, R.
, Pérez-Vidal
, L.
, and Vilaplana-Pastó
, J.
, 2000
, CAD Tools and Algorithms for Product Design
, 1st ed., P.
Brunet
, C.
Hoffmann
, and D.
Roller
, eds., Springer
, Berlin
, pp. 165
–177
.57.
Makhlouf
, A. B.
, Louhichi
, B.
, Mahjoub
, M. A.
, and Deneux
, D.
, 2019
, “Reconstruction of a CAD Model From the Deformed Mesh Using B-Spline Surfaces
,” Int. J. Comput. Integr. Manuf.
, 32
(7
), pp. 669
–681
. 58.
Raja
, F.
, 2019
, “Evaluation of Properties of Triply Periodic Minimal Surface Structures Using ANSYS
,” Master thesis
, Arizona State University
, Tempe, AZ
.59.
Martin
, W.
, Cohen
, E.
, Fish
, R.
, and Shirley
, P.
, 2000
, “Practical Ray Tracing of Trimmed NURBS Surfaces
,” J. Graph. Tools
, 5
(1
), pp. 27
–52
. 60.
Raviv
, A.
, and Elber
, G.
, 2001
, “Interactive Direct Rendering of Trivariate B-Spline Scalar Functions
,” IEEE Trans. Vis. Comput. Graph.
, 7
(2
), pp. 109
–119
. 61.
Velivela
, P. T.
, 2018
, “Masking Materials and Bio-Inspired Caps for Chemical Etching of Dental Implants
,” Politecnico di Milano, https://www.politesi.polimi.it/handle/10589/14313562.
Autumn
, K.
, Liang
, Y. A.
, Tonia Hsieh
, S.
, Zesch
, W.
, Chan
, W. P.
, Kenny
, T. W.
, Fearing
, R.
, and Full
, R. J.
, 2000
, “Adhesive Force of a Single Gecko Foot-Hair
,” Nature
, 405
(6787
), pp. 681
–685
. 63.
Autumn
, K.
, Sitti
, M.
, Liang
, Y. A.
, Peattie
, A. M.
, Hansen
, W. R.
, Sponberg
, S.
, Kenny
, T. W.
, Fearing
, R.
, Israelachvili
, J. N.
, and Full
, R. J.
, 2002
, “Evidence for van Der Waals Adhesion in Gecko Setae
,” Proc. Natl. Acad. Sci. U.S.A.
, 99
(19
), pp. 12252
–12256
. 64.
Song
, Y.
, Dai
, Z.
, Wang
, Z.
, Ji
, A.
, and Gorb
, S. N.
, 2016
, “The Synergy Between the Insect-Inspired Claws and Adhesive Pads Increases the Attachment Ability on Various Rough Surfaces
,” Sci. Rep.
, 6
(1
), p. 26219
. 65.
Federle
, W.
, Riehle
, M.
, Curtis
, A. S. G.
, and Full
, R. J.
, 2002
, “An Integrative Study of Insect Adhesion: Mechanics and Wet Adhesion of Pretarsal Pads in Ants
,” Integr. Comput. Biol.
, 42
(6
), pp. 1100
–1106
. 66.
Huang
, J.
, Chiam
, S. Y.
, Tan
, H. H.
, Wang
, S.
, and Chim
, W. K.
, 2010
, “Fabrication of Silicon Nanowires With Precise Diameter Control Using Metal Nanodot Arrays as a Hard Mask Blocking Material in Chemical Etching
,” Chem. Mater.
, 22
(13
), pp. 4111
–4116
. 67.
Alsheghri
, A.
, Reznikov
, N.
, Piché
, N.
, McKee
, M. D.
, Tamimi
, F.
, and Song
, J.
, 2021
, “Optimization of 3D Network Topology for Bioinspired Design of Stiff and Lightweight Bone-Like Structures
,” Mater. Sci. Eng. C
, 123
, p. 112010
. 68.
Liu
, K.
, and Jiang
, L.
, 2011
, “Bio-Inspired Design of Multiscale Structures for Function Integration
,” Nano Today
, 6
(2
), pp. 155
–175
. 69.
Schmidt-Nielsen
, B.
, Schmidt-Nielsen
, K.
, Houpt
, T. R.
, and Jarnum
, S. A.
, 1956
, “Water Balance of the Camel
,” Am. J. Physiol. Legacy Content
, 185
(1
), pp. 185
–194
. 70.
Han
, Z.
, Mu
, Z.
, Yin
, W.
, Li
, W.
, Niu
, S.
, Zhang
, J.
, and Ren
, L.
, 2016
, “Biomimetic Multifunctional Surfaces Inspired From Animals
,” Adv. Colloid Interface Sci.
, 234
, pp. 27
–50
. 71.
Nagy
, K. A.
, 2004
, “Water Economy of Free-Living Desert Animals
,” Int. Congr. Ser.
, 1275
, pp. 291
–297
. 72.
Youssef
, B. B.
, 2013
, Procedia Computer Science
, V.
Alexandrov
, M.
Lees
, V.
Krzhizhanovskaya
, J.
Dongarra
, and P. M. A.
Sloot
, eds., Elsevier
, Baltimore, MD
, pp. 391
–398
.73.
Fantini
, M.
, Curto
, M.
, and De Crescenzio
, F.
, 2016
, “A Method to Design Biomimetic Scaffolds for Bone Tissue Engineering Based on Voronoi Lattices
,” Virtual Phys. Prototyp.
, 11
(2
), pp. 77
–90
. 74.
Gómez-Gálvez
, P.
, Vicente-Munuera
, P.
, Tagua
, A.
, Forja
, C.
, Castro
, A. M.
, Letrán
, M.
, Valencia-Expósito
, A.
, Grima
, C.
, Bermúdez-Gallardo
, M.
, Serrano-Pérez-Higueras
, Ó.
, Cavodeassi
, F.
, Sotillos
, S.
, Martín-Bermudo
, M. D.
, Márquez
, A.
, Buceta
, J.
, and Escudero
, L. M.
, 2018
, “Scutoids Are a Geometrical Solution to Three-Dimensional Packing of Epithelia
,” Nat. Commun.
, 9
(1
), p. 2960
. 75.
Strand
, R.
, 2004
, “Surface Skeletons in Grids With Non-Cubic Voxels
,” Proceedings of the 17th International Conference on Pattern Recognition (ICPR 2004)
, Cambridge, UK
, Aug. 26
, IEEE, Vol. 1, pp. 548
–551
.76.
Laine
, S.
, and Karras
, T.
, 2011
, “Efficient Sparse Voxel Octrees
,” IEEE Trans. Vis. Comput. Graph.
, 17
(8
), pp. 1048
–1059
. 77.
Schulz
, H.
, 2009
, “Polyhedral Approximation and Practical Convex Hull Algorithm for Certain Classes of Voxel Sets
,” Discret. Appl. Math.
, 157
(16
), pp. 3485
–3493
. 78.
Minc
, N.
, Burgess
, D.
, and Chang
, F.
, 2011
, “Influence of Cell Geometry on Division-Plane Positioning
,” Cell
, 144
(3
), pp. 414
–426
. 79.
Schmick
, M.
, and Bastiaens
, P. I. H.
, 2014
, “The Interdependence of Membrane Shape and Cellular Signal Processing
,” Cell
, 156
(6
), pp. 1132
–1138
. 80.
Kils
, U.
, 1983
, “Swimming and Feeding of Antarctic Krill, Euphausia Superba—Some Outstanding Energetics and Dynamics—Some Unique Morphological Details
,” Ber. Polarforsch.
, 4
, pp. 130
–155
.81.
Zhang
, W.
, Chen
, X.-X.
, Liu
, Y.-M.
, Liu
, D.-Y.
, Du
, Y.-F.
, Chen
, X.-P.
, and Zou
, C.-Q.
, 2018
, “The Role of Phosphorus Supply in Maximizing the Leaf Area, Photosynthetic Rate, Coordinated to Grain Yield of Summer Maize
,” Field Crops Res.
, 219
, pp. 113
–119
. 82.
Jørgensen
, S. E.
, 2002
, “Explanation of Ecological Rules and Observation by Application of Ecosystem Theory and Ecological Models
,” Ecol. Modell.
, 158
(3
), pp. 241
–248
. 83.
Yang
, X. S.
, and Zhang
, J. J.
, 2005
, “Modelling and Animating Hand Wrinkles
,” 5th International Conference on Computational Science—ICCS 2005
, Atlanta, GA
, May 22–25
, Springer-Verlag
, Berlin/Heidelberg
, pp. 199
–206
.84.
d’Eon
, E.
, Luebke
, D.
, and Enderton
, E.
, 2007
, “Efficient Rendering of Human Skin
,” Proceedings of the 18th Eurographics Conference on Rendering Techniques, EGSR’07
, Goslar, Germany
, June 25–27
, pp. 147
–157
.85.
Altair Acquires SIMSOLID
, 2018
, “Altair Engineering
,” https://www.altair.com/newsdetail/?news_id=1155586.
Zbiciak
, R.
, and Grabowik
, C.
, 2017
, “Feature Recognition Methods Review
,” Proceedings of the 13th International Scientific Conference. RESRB 2016. Lecture Notes in Mechanical Engineering
, E.
Rusiński
, and D.
Pietrusiak
, eds., Springer
, Cham
, pp. 605
–615
.87.
Aremu
, A. O.
, Brennan-Craddock
, J. P. J.
, Panesar
, A.
, Ashcroft
, I. A.
, Hague
, R. J. M.
, Wildman
, R. D.
, and Tuck
, C.
, 2017
, “A Voxel-Based Method of Constructing and Skinning Conformal and Functionally Graded Lattice Structures Suitable for Additive Manufacturing
,” Addit. Manuf.
, 13
, pp. 1
–13
. 88.
He
, T.
, Hong
, L.
, Kaufman
, A.
, Varshney
, A.
, and Wang
, S.
, 1995
, “Voxel Based Object Simplification
,” Proceedings Visualization’95
, Monterey, CA
, Oct. 29– Nov. 3
, IEEE Computer Society Press
, pp. 296
–303
.89.
Nooruddin
, F. S.
, and Turk
, G.
, 2003
, “Simplification and Repair of Polygonal Models Using Volumetric Techniques
,” IEEE Trans. Vis. Comput. Graph.
, 9
(2
), pp. 191
–205
. 90.
Telea
, A.
, and Jalba
, A.
, 2011
, “Voxel-Based Assessment of Printability of 3D Shapes
,” Proceedings of the 10th International Conference on Mathematical Morphology and Its Applications to Image and Signal Processing
, Berlin, Germany
, July 6–8
, Springer-Verlag, pp. 393
–404
.91.
Gobert
, C.
, Reutzel
, E. W.
, Petrich
, J.
, Nassar
, A. R.
, and Phoha
, S.
, 2018
, “Application of Supervised Machine Learning for Defect Detection During Metallic Powder Bed Fusion Additive Manufacturing Using High Resolution Imaging
,” Addit. Manuf.
, 21
, pp. 517
–528
. 92.
Lorensen
, W. E.
, and Cline
, H. E.
, 1987
, “Marching Cubes: A High Resolution 3D Surface Construction Algorithm
,” ACM SIGGRAPH Comput. Graph.
, 21
(4
), pp. 163
–169
. 93.
Newman
, T. S.
, and Yi
, H.
, 2006
, “A Survey of the Marching Cubes Algorithm
,” Comput. Graph.
, 30
(5
), pp. 854
–879
. 94.
Adalsteinsson
, D.
, and Sethian
, J. A.
, 1995
, “A Fast Level Set Method for Propagating Interfaces
,” J. Comput. Phys.
, 118
(2
), pp. 269
–277
. 95.
Kauker
, D.
, Falk
, M.
, Reina
, G.
, Ynnerman
, A.
, and Ertl
, T.
, 2016
, “VoxLink—Combining Sparse Volumetric Data and Geometry for Efficient Rendering
,” Comput. Vis. Media
, 2
(1
), pp. 45
–56
. 96.
Marcus
, R. C.
, 2017
, “Level-of-Detail Independent Voxel-Based Surface Approximations
,” Utrecht University
, https://dspace.library.uu.nl/handle/1874/34881897.
Rom
, M.
, and Brakhage
, K.-H.
, 2011
, Volume Mesh Generation for Numerical Flow Simulations Using Catmull-Clark and Surface Approximation Methods.
, Institut für Geometrie und Praktische Mathematik
, Aachen
.98.
Fuchs
, R.
, Welker
, V.
, and Hornegger
, J.
, 2010
, “Non-Convex Polyhedral Volume of Interest Selection
,” Comput. Med. Imag. Graph.
, 34
(2
), pp. 105
–113
. 99.
Massarwi
, F.
, and Elber
, G.
, 2016
, “A B-Spline Based Framework for Volumetric Object Modeling
,” Comput. Aided Des.
, 78
, pp. 36
–47
. 100.
Wassermann
, B.
, Korshunova
, N.
, Kollmannsberger
, S.
, Rank
, E.
, and Elber
, G.
, 2020
, “Finite Cell Method for Functionally Graded Materials Based on V-Models and Homogenized Microstructures
,” Adv. Model. Simul. Eng. Sci.
, 7
(1
), p. 49
. 101.
Antolin
, P.
, Buffa
, A.
, and Martinelli
, M.
, 2019
, “Isogeometric Analysis on V-Reps: First Results
,” Comput. Methods Appl. Mech. Eng.
, 355
, pp. 976
–1002
. 102.
Massarwi
, F.
, Antolin
, P.
, and Elber
, G.
, 2019
, “Volumetric Untrimming: Precise Decomposition of Trimmed Trivariates Into Tensor Products
,” Comput. Aided Geom. Des.
, 71
, pp. 1
–15
. 103.
Burkhart
, D.
, Hamann
, B.
, and Umlauf
, G.
, 2010
, “Iso-Geometric Finite Element Analysis Based on Catmull-Clark Subdivision Solids
,” Comput. Graph. Forum
, 29
(5
), pp. 1575
–1584
. 104.
Hahmann
, S.
, Bonneau
, G.-P.
, Barbier
, S.
, Elber
, G.
, and Hagen
, H.
, 2012
, “Volume-Preserving FFD for Programmable Graphics Hardware
,” Vis. Comput.
, 28
(3
), pp. 231
–245
. 105.
Ma
, H.
, and Schewe
, K.-D.
, 2011
, “Conceptual Geometric Modelling,” Handbook of Conceptual Modeling
, D. W.
Embley
, and B.
Thalheim
, eds., Springer
, Berlin
, pp. 421
–440
.106.
Chen
, F.
, Dokken
, C.
, Grandine
, T. A.
, and Morin
, G.
, 2017
, “Geometric Modelling, Interoperability and New Challenges (Dagstuhl Seminar 17221)
,” Dagstuhl Rep.
, 7
(5
), pp. 140
–168
. 107.
Rawson
, S. D.
, Margetts
, L.
, Wong
, J. K. F.
, and Cartmell
, S. H.
, 2015
, “Sutured Tendon Repair; a Multi-Scale Finite Element Model
,” Biomech. Model. Mechanobiol.
, 14
(1
), pp. 123
–133
. 108.
Luebke
, D.
, Reddy
, M.
, Cohen
, J. D.
, Varshney
, A.
, Watson
, B.
, and Huebner
, R.
, 2002
, Level of Detail for 3D Graphics
, Elsevier
, New York, NY
.109.
Borrmann
, A.
, Kolbe
, T. H.
, Donaubauer
, A.
, Steuer
, H.
, Jubierre
, J. R.
, and Flurl
, M.
, 2015
, “Multi-Scale Geometric-Semantic Modeling of Shield Tunnels for GIS and BIM Applications
,” Comput. Aided Civ. Infrastruct. Eng.
, 30
(4
), pp. 263
–281
. 110.
Agugiaro
, G.
, Remondino
, F.
, Girardi
, G.
, von Schwerin
, J.
, Richards-Rissetto
, H.
, and De Amicis
, R.
, 2011
, “A Web-Based Interactive Tool for Multi-Resolution 3D Models of a Maya Archaeological Site
,” Int. Arch. Photogram. Remote Sens. Spatial Inf. Sci.
, XXXVIII-5
, pp. 23
–30
. 111.
Sacks
, M. S.
, Khalighi
, A.
, Rego
, B.
, Ayoub
, S.
, and Drach
, A.
, 2017
, “On the Need for Multi-Scale Geometric Modelling of the Mitral Heart Valve
,” Healthc. Technol. Lett.
, 4
(5
), p. 150
. 112.
Tian
, F.
, Hua
, W.
, Dong
, Z.
, and Bao
, H.
, 2010
, “Adaptive Voxels: Interactive Rendering of Massive 3D Models
,” Vis. Comput.
, 26
(6–8
), pp. 409
–419
. 113.
Limper
, M.
, Jung
, Y.
, Behr
, J.
, and Alexa
, M.
, 2013
, “The POP Buffer: Rapid Progressive Clustering by Geometry Quantization
,” Comput. Graph. Forum
, 32
(7
), pp. 197
–206
. 114.
0 FPS
, 2018
, “A Level of Detail Method for Blocky Voxels
,” https://0fps.net/2018/03/03/a-level-of-detail-method-for-blocky-voxels/115.
Seemann
, P.
, Fuhrmann
, S.
, Guthe
, S.
, Langguth
, F.
, and Goesele
, M.
, 2016
, “Simplification of Multi-Scale Geometry Using Adaptive Curvature Fields
,” http://arxiv.org/abs/1610.07368116.
Tao
, W.
, and Leu
, M. C.
, 2016
, “Design of Lattice Structure for Additive Manufacturing
,” 2016 International Symposium on Flexible Automation (ISFA)
, Cleveland, OH
, Aug. 1–3
, IEEE, pp. 325
–332
.117.
Dong
, G.
, Tang
, Y.
, and Zhao
, Y. F.
, 2017
, “A Survey of Modeling of Lattice Structures Fabricated by Additive Manufacturing
,” ASME J. Mech. Des.
, 139
(10
), p. 100906
. 118.
Frulloni
, E.
, Kenny
, J. M.
, Conti
, P.
, and Torre
, L.
, 2007
, “Experimental Study and Finite Element Analysis of the Elastic Instability of Composite Lattice Structures for Aeronautic Applications
,” Compos. Struct.
, 78
(4
), pp. 519
–528
. 119.
Martínez
, J.
, Dumas
, J.
, and Lefebvre
, S.
, 2016
, “Procedural Voronoi Foams for Additive Manufacturing
,” ACM Trans. Graph.
, 35
(4
), pp. 44:1
–44:12
. 120.
Schumacher
, C.
, Bickel
, B.
, Rys
, J.
, Marschner
, S.
, Daraio
, C.
, and Gross
, M.
, 2015
, “Microstructures to Control Elasticity in 3D Printing
,” ACM Trans. Graph.
, 34
(4
), pp. 1
–13
. 121.
Tang
, Y.
, Dong
, G.
, and Zhao
, Y. F.
, 2019
, “A Hybrid Geometric Modeling Method for Lattice Structures Fabricated by Additive Manufacturing
,” Int. J. Adv. Manuf. Technol.
, 102
(9–12
), pp. 4011
–4030
. 122.
Liu
, Y.
, Zhuo
, S.
, Xiao
, Y.
, Zheng
, G.
, Dong
, G.
, and Zhao
, Y. F.
, 2020
, “Rapid Modeling and Design Optimization of Multi-Topology Lattice Structure Based on Unit-Cell Library
,” ASME J. Mech. Des.
, 142
(9
), p. 091705
. 123.
Liu
, Y.
, Zheng
, G.
, Letov
, N.
, and Zhao
, Y. F.
, 2020
, “A Survey of Modeling and Optimization Methods for Multi-Scale Heterogeneous Lattice Structures
,” ASME J. Mech. Des.
, 143
(4
), p. 040803
. 124.
An
, X.
, and Fan
, H.
, 2016
, “Hybrid Design and Energy Absorption of Luffa-Sponge-Like Hierarchical Cellular Structures
,” Mater. Des.
, 106
, pp. 247
–257
. 125.
Douglas
, T.
, 2003
, “A Bright Bio-Inspired Future
,” Science
, 299
(5610
), pp. 1192
–1193
. 126.
Jang
, K.-I.
, Chung
, H. U.
, Xu
, S.
, Lee
, C. H.
, Luan
, H.
, Jeong
, J.
, Cheng
, H.
, Kim
, G.-T.
, Han
, S. Y.
, Lee
, J. W.
, Kim
, J.
, Cho
, M.
, Miao
, F.
, Yang
, Y.
, Jung
, H. N.
, Flavin
, M.
, Liu
, H.
, Kong
, G. W.
, Yu
, K. J.
, Rhee
, S. I.
, Chung
, J.
, Kim
, B.
, Kwak,
J. W.
, Yun
, M. H.
, Kim
, J. Y.
, Song
, Y. M.
, Paik
, U.
, Zhang
, Y.
, Huang
, Y.
, and Rogers
, J. A.
, 2015
, “Soft Network Composite Materials With Deterministic and Bio-Inspired Designs
,” Nat. Commun.
, 6
(1
), p. 6566
. 127.
Naboni
, R.
, and Kunic
, A.
, 2017
, “Design and Additive Manufacturing of Lattice-Based Cellular Solids at Building Scale
,” Blucher Design Proceedings
, Concepción, Chile
, Nov. 22–24
, pp. 369
–375
.128.
Zheng
, Y.
, 2019
, Bioinspired Design of Materials Surfaces
, K. D.
Santos
, ed., 1st ed., Elsevier
, Cambridge, MA
, pp. 27
–97
.129.
Liu
, K.
, Yao
, X.
, and Jiang
, L.
, 2010
, “Recent Developments in Bio-Inspired Special Wettability
,” Chem. Soc. Rev.
, 39
(8
), p. 3240
. 130.
Hancock
, M. J.
, Sekeroglu
, K.
, and Demirel
, M. C.
, 2012
, “Bioinspired Directional Surfaces for Adhesion, Wetting, and Transport
,” Adv. Funct. Mater.
, 22
(11
), pp. 2223
–2234
. 131.
Liu
, K.
, Cao
, M.
, Fujishima
, A.
, and Jiang
, L.
, 2014
, “Bio-Inspired Titanium Dioxide Materials With Special Wettability and Their Applications
,” Chem. Rev.
, 114
(19
), pp. 10044
–10094
. 132.
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
. 133.
Kucewicz
, M.
, Baranowski
, P.
, Małachowski
, J.
, Popławski
, A.
, and Płatek
, P.
, 2018
, “Modelling, and Characterization of 3D Printed Cellular Structures
,” Mater. Des.
, 142
, pp. 177
–189
. 134.
Lozanovski
, B.
, Leary
, M.
, Tran
, P.
, Shidid
, D.
, Qian
, M.
, Choong
, P.
, and Brandt
, M.
, 2019
, “Computational Modelling of Strut Defects in SLM Manufactured Lattice Structures
,” Mater. Des.
, 171
, p. 107671
. 135.
Leonardi
, F.
, Graziosi
, S.
, Casati
, R.
, Tamburrino
, F.
, and Bordegoni
, M.
, 2019
, “Additive Manufacturing of Heterogeneous Lattice Structures: An Experimental Exploration
,” Proc. Des. Soc.: Int. Conf. Eng. Des.
, 1
(1
), pp. 669
–678
. 136.
Gümrük
, R.
, and Mines
, R. A. W.
, 2013
, “Compressive Behaviour of Stainless Steel Micro-Lattice Structures
,” Int. J. Mech. Sci.
, 68
, pp. 125
–139
. 137.
Kale
, S.
, Khani
, N.
, Nadernezhad
, A.
, and Koc
, B.
, 2017
, “Modeling and Additive Manufacturing of Biomimetic Heterogeneous Scaffold
,” Procedia CIRP
, 65
, pp. 48
–55
. 138.
Tang
, Y.
, Dong
, G.
, Zhou
, Q.
, and Zhao
, Y. F.
, 2018
, “Lattice Structure Design and Optimization With Additive Manufacturing Constraints
,” IEEE Trans. Autom. Sci. Eng.
, 15
(4
), pp. 1546
–1562
. 139.
Yang
, S.
, Tang
, Y.
, and Zhao
, Y. F.
, 2015
, “A New Part Consolidation Method to Embrace the Design Freedom of Additive Manufacturing
,” J. Manuf. Process.
, 20
, pp. 444
–449
. 140.
141.
Tang
, Y.
, Yang
, S.
, and Zhao
, Y. F.
, 2016
, “Design Method for Conformal Lattice-Skin Structure Fabricated by AM Technologies
,” Volume 1A: 36th Computers and Information in Engineering Conference
, Charlotte, NC
, Aug. 21–24
, American Society of Mechanical Engineers
, p. V01AT02A037
.142.
143.
García-Dominguez
, A.
, Claver
, J.
, and Sebastián
, M. A.
, 2020
, “Optimization Methodology for Additive Manufacturing of Customized Parts by Fused Deposition Modeling (FDM). Application to a Shoe Heel
,” Polymers
, 12
(9
), p. 2119
. 144.
General Lattice
, 2020
, “Additive Manufacturing—Design Studion
,” Studio, https://www.generallattice.com/studio145.
Wehner
, M.
, Truby
, R. L.
, Fitzgerald
, D. J.
, Mosadegh
, B.
, Whitesides
, G. M.
, Lewis
, J. A.
, and Wood
, R. J.
, 2016
, “An Integrated Design and Fabrication Strategy for Entirely Soft, Autonomous Robots
,” Nature
, 536
(7617
), pp. 451
–455
. 146.
Chen
, W.
, Zheng
, X.
, and Liu
, S.
, 2018
, “Finite-Element-Mesh Based Method for Modeling and Optimization of Lattice Structures for Additive Manufacturing
,” Materials
, 11
(11
), p. 2073
. 147.
University of Alberta
, 2001
, “University of Alberta ANSYS Tutorial
,” ANSYS Command File Programming Features, https://sites.ualberta.ca/~wmoussa/AnsysTutorial/CL/Features.html148.
Portela
, C. M.
, Greer
, J. R.
, and Kochmann
, D. M.
, 2018
, “Impact of Node Geometry on the Effective Stiffness of Non-Slender Three-Dimensional Truss Lattice Architectures
,” Extreme Mech. Lett.
, 22
, pp. 138
–148
. 149.
Savio
, G.
, Meneghello
, R.
, and Concheri
, G.
, 2019
, “Design of Variable Thickness Triply Periodic Surfaces for Additive Manufacturing
,” Prog. Addit. Manuf.
, 4
(3
), pp. 281
–290
. 150.
Pasko
, A.
, Fryazinov
, O.
, Vilbrandt
, T.
, Fayolle
, P.-A.
, and Adzhiev
, V.
, 2011
, “Procedural Function-Based Modelling of Volumetric Microstructures
,” Graph. Models
, 73
(5
), pp. 165
–181
. 151.
Cartwright
, R.
, Adzhiev
, V.
, Pasko
, A. A.
, Goto
, Y.
, and Kunii
, T. L.
, 2005
, “Web-Based Shape Modeling With HyperFun
,” IEEE Comput. Graph. Appl.
, 25
(2
), pp. 60
–69
. 152.
Yang
, N.
, Tian
, Y.
, and Zhang
, D.
, 2015
, “Novel Real Function Based Method to Construct Heterogeneous Porous Scaffolds and Additive Manufacturing for Use in Medical Engineering
,” Med. Eng. Phys.
, 37
(11
), pp. 1037
–1046
. 153.
Li
, D.
, Liao
, W.
, Dai
, N.
, Dong
, G.
, Tang
, Y.
, and Xie
, Y. M.
, 2018
, “Optimal Design and Modeling of Gyroid-Based Functionally Graded Cellular Structures for Additive Manufacturing
,” Comput. Aided Des.
, 104
, pp. 87
–99
. 154.
Wang
, Y.
, Zhang
, L.
, Daynes
, S.
, Zhang
, H.
, Feih
, S.
, and Wang
, M. Y.
, 2018
, “Design of Graded Lattice Structure With Optimized Mesostructures for Additive Manufacturing
,” Mater. Des.
, 142
, pp. 114
–123
. 155.
Liu
, X.
, and Shapiro
, V.
, 2018
, “Multiscale Shape–Material Modeling by Composition
,” Comput. Aided Des.
, 102
, pp. 194
–203
. 156.
Schoen
, A. H.
, 1970
, Infinite Periodic Minimal Surfaces Without Self-Intersections
, National Aeronautics and Space Administration (NASA)
, Washington, DC
.157.
Gan
, Z.
, Turner
, M. D.
, and Gu
, M.
, 2016
, “Biomimetic Gyroid Nanostructures Exceeding Their Natural Origins
,” Sci. Adv.
, 2
(5
), p. e1600084
. 158.
Longley
, W.
, and McIntosh
, T. J.
, 1983
, “A Bicontinuous Tetrahedral Structure in a Liquid-Crystalline Lipid
,” Nature
, 303
(5918
), pp. 612
–614
. 159.
Adzhiev
, V.
, Cartwright
, R.
, Fausett
, E.
, Ossipov
, A.
, Pasko
, A. A.
, and Savchenko
, V. V.
, 1999
, “HyperFun Project: Language and Software Tools for F-Rep Shape Modeling
,” Comput. Graph. Geom.
, 1
, pp. 75
–100
.160.
Tereshin
, A.
, Adzhiev
, V.
, Fryazinov
, O.
, and Pasko
, A.
, 2019
, “Hybrid Function Representation With Distance Properties,” Eurographics 2019—Short Papers
, P.
Cignoni
, and E.
Miguel
, eds., The Eurographics Association
, Genoa
, pp. 17
–20
.161.
Katopodes
, N. D.
, 2019
, Free-Surface Flow
, K.
McCombs
, ed., Elsevier
, New York
, pp. 804
–828
.162.
Kawamoto
, R.
, Andò
, E.
, Viggiani
, G.
, and Andrade
, J. E.
, 2016
, “Level Set Discrete Element Method for Three-Dimensional Computations With Triaxial Case Study
,” J. Mech. Phys. Solids
, 91
, pp. 1
–13
. 163.
Miyamoto
, Y.
, Kaysser
, W. A.
, Rabin
, B. H.
, Kawasaki
, A.
, and Ford
, R. G.
, 2013
, Functionally Graded Materials: Design, Processing and Applications
, Springer Science & Business Media
, Berlin, Germany
.164.
Boyer
, C. B.
, and Merzbach
, U. C.
, 1991
, A History of Mathematics
, 2nd ed., Wiley
, New York
.165.
Egan
, P.
, Sinko
, R.
, LeDuc
, P. R.
, and Keten
, S.
, 2015
, “The Role of Mechanics in Biological and Bio-Inspired Systems
,” Nat. Commun.
, 6
(1
), p. 7418
. 166.
Voss
, R. F.
, 1988
, “Fractals in Nature: From Characterization to Simulation,” The Science of Fractal Images
, H.-O.
Peitgen
, and D.
Saupe
, eds., Springer
, New York
, pp. 21
–70
.167.
Zhou
, Z.
, Alégot
, H.
, and Irvine
, K. D.
, 2019
, “Oriented Cell Divisions Are Not Required for Drosophila Wing Shape
,” Curr. Biol.
, 29
(5
), pp. 856
–864.e3
. 168.
Cheng
, L.
, Bai
, J.
, and To
, A. C.
, 2019
, “Functionally Graded Lattice Structure Topology Optimization for the Design of Additive Manufactured Components With Stress Constraints
,” Comput. Methods Appl. Mech. Eng.
, 344
, pp. 334
–359
. 169.
ANSI
, 2016
, “ISO 10303-21:2016. Industrial Automation Systems and Integration—Product Data Representation and Exchange—Part 21: Implementation Methods: Clear Text Encoding of the Exchange Structure
,” ANSI, https://webstore.ansi.org/Standards/ISO/ISO10303212016170.
Chang
, K.-H.
, 2014
, Product Design Modeling Using CAD/CAE: The Computer Aided Engineering Design Series
, Academic Press
, Cambridge, MA
.171.
Grimm
, T.
, 2004
, User’s Guide to Rapid Prototyping
, Society of Manufacturing Engineers
, Southfield, MI
.172.
PTC
, 2019
, “Material Homogenization for Lattice Simulation in Additive Manufacturing
,” https://support.ptc.com/help/creo/creo_pma/r6.0/usascii/whats_new_pma/addmanu-material_homogenization_lattice_simulation.html173.
Zheng
, X.
, Smith
, W.
, Jackson
, J.
, Moran
, B.
, Cui
, H.
, Chen
, D.
, Ye
, J.
, Fang
, N.
, Rodriguez
, N.
, Weisgraber
, T.
, and Spadaccini
, C. M.
, 2016
, “Multiscale Metallic Metamaterials
,” Nat. Mater.
, 15
(10
), pp. 1100
–1106
. 174.
Antolin
, P.
, Buffa
, A.
, Cohen
, E.
, Dannenhoffer
, J. F.
, Elber
, G.
, Elgeti
, S.
, Haimes
, R.
, and Riesenfeld
, R.
, 2019
, “Optimizing Micro-Tiles in Micro-Structures as a Design Paradigm
,” Comput. Aided Des.
, 115
, pp. 23
–33
. 175.
Liu
, T.-L.
, Upadhyayula
, S.
, Milkie
, D. E.
, Singh
, V.
, Wang
, K.
, Swinburne
, I. A.
, Mosaliganti
, K. R.
, Collins
, Z. M.
, Hiscock
, T. W.
, Shea
, J.
, Kohrman
, A. Q.
, Medwig
, T. N.
, Dambournet
, D.
, Forster
, R.
, Cunniff
, B.
, Ruan
, Y.
, Yashiro
, H.
, Scholpp
, S.
, Meyerowitz
, E. M.
, Hockemeyer
, D.
, Drubin
, D. G.
, Martin
, B. L.
, Matus
, D. Q.
, Koyama
, M.
, Megason
, S. G.
, Kirchhausen
, T.
, and Betzig
, E.
, 2018
, “Observing the Cell in Its Native State: Imaging Subcellular Dynamics in Multicellular Organisms
,” Science
, 360
(6386
), p. eaaq1392
. 176.
Smith
, H. F.
, Parker
, W.
, Kotzé
, S. H.
, and Laurin
, M.
, 2017
, “Morphological Evolution of the Mammalian Cecum and Cecal Appendix
,” C.R. Palevol
, 16
(1
), pp. 39
–57
. 177.
Bass
, L.
, Clements
, P.
, and Kazman
, R.
, 2013
, Software Architecture in Practice
, SEI Series in Software Engineering, Addison-Wesley
, Upper Saddle River, NJ
.178.
C3D Labs
, 2020
, “Multi-Thread Support Arrives in C3D Toolkit
,” C3D Toolkit, https://c3dlabs.com/en/blog/tech-tips/multi-thread-support-arrives-in-c3d-toolkit/179.
Urbańczyk
, A.
, Wright
, J.
, Cowden
, D.
, Solutions
, I. T.
, Özderya
, H. Y.
, Boyd
, M.
, Agostini
, B.
, Greminger
, M.
, Buchanan
, J.
, León Peque
, M. S.
, de, Boin
, P.
, Saville
, W.
, Weissinger
, B.
, Osterwood
, C.
, Kono
, A.
, Levering
, H.
, Turner
, W.
, Trhoň
, A.
, Christoforo
, G.
, Peterson
, A.
, Grunichev
, A.
, Gregg-Smith
, A.
, and Anderson
, A.
, 2021
, “CadQuery 2.1
,” CadQuery/Cadquery
. Copyright © 2021 by ASME
You do not currently have access to this content.
