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Philosophical Magazine Letters Volume 83, 2003 - Issue 3
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Original Articles

Topological interlocking of platonic solids: A way to new materials and structures

A. V. Dyskin Department of Civil and Resource Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia, 6009, Australia
,
Y. Estrin Department of Civil and Resource Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia, 6009, Australia; Institut für Werkstoffkunde und Werkstofftechnik, Technische Universität Clausthal, Clausthal-Zellerfeld, D-38678, Germany
,
A. J. Kanel-Belov Department of Civil and Resource Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia, 6009, Australia
&
E. Pasternak Department of Civil and Resource Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia, 6009, Australia
Pages 197-203 | Published online: 14 Nov 2010

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Jun Wang & Rahul Rai. (2022) Generative design of conformal cubic periodic cellular structures using a surrogate model-based optimisation scheme. International Journal of Production Research 60:5, pages 1458-1477.
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F. Barthelat. (2015) Architectured materials in engineering and biology: fabrication, structure, mechanics and performance. International Materials Reviews 60:8, pages 413-430.
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Arcady V. Dyskin & Elena Pasternak. (2012) Mechanical effect of rotating non-spherical particles on failure in compression. Philosophical Magazine 92:28-30, pages 3451-3473.
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M. F. Ashby . (2005) Hybrids to fill holes in material property space. Philosophical Magazine 85:26-27, pages 3235-3257.
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Articles from other publishers (69)

Silvan Ullmann, David S. Kammer & Shai Feldfogel. (2024) The Deflection Limit of Slab-Like Topologically Interlocked Structures. Journal of Applied Mechanics 91:2.
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Elham Kiyani, Hamidreza Yazdani Sarvestani, Hossein Ravanbakhsh, Razyeh Behbahani, Behnam Ashrafi, Meysam Rahmat & Mikko Karttunen. (2023) Designing architectured ceramics for transient thermal applications using finite element and deep learning. Modelling and Simulation in Materials Science and Engineering 32:1, pages 015001.
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Igor Shufrin, Elena Pasternak & Arcady Dyskin. (2023) Environmentally Friendly Smart Construction—Review of Recent Developments and Opportunities. Applied Sciences 13:23, pages 12891.
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Ioannis Koureas, Mohit Pundir, Shai Feldfogel & David S. Kammer. (2023) The key to the enhanced performance of slab-like topologically interlocked structures with non-planar blocks. International Journal of Solids and Structures 285, pages 112523.
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Matthew Ebert, Ergun Akleman, Vinayak Krishnamurthy, Roman Kulagin & Yuri Estrin. (2023) VoroNoodles: Topological Interlocking with Helical Layered 2‐Honeycombs. Advanced Engineering Materials.
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Shai Feldfogel, Konstantinos Karapiperis, Jose Andrade & David S. Kammer. (2023) Scaling, saturation, and upper bounds in the failure of topologically interlocked structures. International Journal of Solids and Structures 269, pages 112228.
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Tanner Ballance & Thomas Siegmund. (2023) Numerical study on wave propagation in a row of topologically interlocked tetrahedra. Granular Matter 25:1.
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Xudong Yang, Zongzheng Wang, Bojian Zhang, Tianyu Chen, Changhong Linghu, Kunlin Wu, Guohui Wang, Hailu Wang & Yifan Wang. (2022) Self‐Sensing Robotic Structures from Architectured Particle Assemblies. Advanced Intelligent Systems 5:1.
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Ioannis Koureas, Mohit Pundir, Shai Feldfogel & David S. Kammer. (2022) On the failure of beam-like topologically interlocked structures. International Journal of Solids and Structures 259, pages 112029.
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V Ermolai, A Sover & G Nagîţ. (2022) Design and physical validation of a non-planar interlocking element for tubular structures. IOP Conference Series: Materials Science and Engineering 1235:1, pages 012003.
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Yuri Estrin, Vinayak R. Krishnamurthy & Ergun Akleman. (2021) Design of architectured materials based on topological and geometrical interlocking. Journal of Materials Research and Technology 15, pages 1165-1178.
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Francesca Lecci, Cecilia Mazzoli, Cristiana Bartolomei & Riccardo Gulli. (2020) Design of Flat Vaults with Topological Interlocking Solids. Nexus Network Journal 23:3, pages 607-627.
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Ziqi Wang, Peng Song & Mark Pauly. (2021) State of the Art on Computational Design of Assemblies with Rigid Parts. Computer Graphics Forum 40:2, pages 633-657.
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Andrew Williams & Thomas Siegmund. (2021) Mechanics of topologically interlocked material systems under point load: Archimedean and Laves tiling. International Journal of Mechanical Sciences 190, pages 106016.
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Cornelie Leopold. 2021. Handbook of the Mathematics of the Arts and Sciences. Handbook of the Mathematics of the Arts and Sciences 291 316 .
Ahmed S. Dalaq & Francois Barthelat. (2020) Manipulating the geometry of architectured beams for maximum toughness and strength. Materials & Design 194, pages 108889.
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Ergun Akleman, Vinayak R. Krishnamurthy, Chia-An Fu, Sai Ganesh Subramanian, Matthew Ebert, Matthew Eng, Courtney Starrett & Haard Panchal. (2020) Generalized abeille tiles: Topologically interlocked space-filling shapes generated based on fabric symmetries. Computers & Graphics 89, pages 156-166.
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Vianney Loing, Olivier Baverel, Jean-François Caron & Romain Mesnil. (2020) Free-form structures from topologically interlocking masonries. Automation in Construction 113, pages 103117.
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Maciej Piekarski. (2020) Floor Slabs Made from Topologically Interlocking Prefabs of Small Size. Buildings 10:4, pages 76.
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Ahmed S. Dalaq & Francois Barthelat. (2020) Three-Dimensional Laser Engraving for Fabrication of Tough Glass-Based Bioinspired Materials. JOM 72:4, pages 1487-1497.
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Mohammad Mirkhalaf & Hala Zreiqat. (2020) Fabrication and Mechanics of Bioinspired Materials with Dense Architectures: Current Status and Future Perspectives. JOM 72:4, pages 1458-1476.
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Andres Bejarano & Christoph Hoffmann. (2020) TIGER: Topological Interlocking GEneratoR. TIGER: Topological Interlocking GEneratoR.
Ziqi Wang, Peng Song, Florin Isvoranu & Mark Pauly. (2019) Design and structural optimization of topological interlocking assemblies. ACM Transactions on Graphics 38:6, pages 1-13.
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Yuri Estrin, Yan Beygelzimer & Roman Kulagin. (2019) Design of Architectured Materials Based on Mechanically Driven Structural and Compositional Patterning. Advanced Engineering Materials 21:9, pages 1900487.
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Muhammed ImamJulien MeaudSusanta GhoshTrisha Sain. (2019) Improvement of Stiffness and Energy Absorption by Harnessing Hierarchical Interlocking in Brittle Polymer Blocks. Journal of Applied Mechanics 86:5.
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Dumitru Bolcu & Marius Marinel Stănescu. (2019) The Influence of Non-Uniformities on the Mechanical Behavior of Hemp-Reinforced Composite Materials with a Dammar Matrix. Materials 12:8, pages 1232.
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Andres Bejarano & Christoph Hoffmann. (2019) A generalized framework for designing topological interlocking configurations. International Journal of Architectural Computing 17:1, pages 53-73.
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Mohammad Mirkhalaf, Amanul Sunesara, Behnam Ashrafi & Francois Barthelat. (2019) Toughness by segmentation: Fabrication, testing and micromechanics of architectured ceramic panels for impact applications. International Journal of Solids and Structures 158, pages 52-65.
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Cornelie Leopold. 2019. Handbook of the Mathematics of the Arts and Sciences. Handbook of the Mathematics of the Arts and Sciences 1 26 .
Cornelie Leopold. 2019. Handbook of the Mathematics of the Arts and Sciences. Handbook of the Mathematics of the Arts and Sciences 1 26 .
Giuseppe Fallacara, Maurizio Barberio & Micaela Colella. 2019. Architectured Materials in Nature and Engineering. Architectured Materials in Nature and Engineering 423 445 .
Mathias Fantin, Thierry Ciblac & Maurizio Brocato. (2018) Resistance of flat vaults taking their stereotomy into account. Journal of Mechanics of Materials and Structures 13:5, pages 657-677.
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Giuseppe Fallacara & Maurizio Barberio. (2018) An Unfinished Manifesto for Stereotomy 2.0. Nexus Network Journal 20:3, pages 519-543.
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Vera Viana. (2018) From Solid to Plane Tessellations, and Back. Nexus Network Journal 20:3, pages 741-768.
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Mohammad Mirkhalaf, Tao Zhou & Francois Barthelat. (2018) Simultaneous improvements of strength and toughness in topologically interlocked ceramics. Proceedings of the National Academy of Sciences 115:37, pages 9128-9133.
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Babak Zareiyan & Behrokh Khoshnevis. (2017) Effects of interlocking on interlayer adhesion and strength of structures in 3D printing of concrete. Automation in Construction 83, pages 212-221.
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V Y Piirainen & Y Estrin. (2017) New Approach to Road Construction in Oil-Producing Regions of Western Siberia. IOP Conference Series: Earth and Environmental Science 87, pages 072003.
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Lee Djumas, George P. Simon, Yuri Estrin & Andrey Molotnikov. (2017) Deformation mechanics of non-planar topologically interlocked assemblies with structural hierarchy and varying geometry. Scientific Reports 7:1.
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Michael M. Porter, Nakul Ravikumar, Francois Barthelat & Roberto Martini. (2017) 3D-printing and mechanics of bio-inspired articulated and multi-material structures. Journal of the Mechanical Behavior of Biomedical Materials 73, pages 114-126.
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Thomas Siegmund, Francois Barthelat, Raymond Cipra, Ed Habtour & Jaret Riddick. (2016) Manufacture and Mechanics of Topologically Interlocked Material Assemblies. Applied Mechanics Reviews 68:4.
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M. Mirkhalaf, J. Tanguay & F. Barthelat. (2016) Carving 3D architectures within glass: Exploring new strategies to transform the mechanics and performance of materials. Extreme Mechanics Letters 7, pages 104-113.
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Lee Djumas, Andrey Molotnikov, George P. Simon & Yuri Estrin. (2016) Enhanced Mechanical Performance of Bio-Inspired Hybrid Structures Utilising Topological Interlocking Geometry. Scientific Reports 6:1.
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Ji Yun Kang, Jung Gi Kim, Hyo Wook Park & Hyoung Seop Kim. (2016) Multiscale architectured materials with composition and grain size gradients manufactured using high-pressure torsion. Scientific Reports 6:1.
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S Khandelwal, T Siegmund, R J Cipra & J S Bolton. (2015) Adaptive mechanical properties of topologically interlocking material systems. Smart Materials and Structures 24:4, pages 045037.
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A Molotnikov, R Gerbrand, Y Qi, G P Simon & Y Estrin. (2015) Design of responsive materials using topologically interlocked elements. Smart Materials and Structures 24:2, pages 025034.
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Maurizio Brocato & Lucia Mondardini. (2015) Parametric analysis of structures from flat vaults to reciprocal grids. International Journal of Solids and Structures 54, pages 50-65.
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Yuezhong Feng, Thomas Siegmund, Ed Habtour & Jaret Riddick. (2015) Impact mechanics of topologically interlocked material assemblies. International Journal of Impact Engineering 75, pages 140-149.
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S. Khandelwal, T. Siegmund, R. J. Cipra & J. S. Bolton. (2014) Scaling of the Elastic Behavior of Two-Dimensional Topologically Interlocked Materials Under Transverse Loading. Journal of Applied Mechanics 81:3.
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Mateus Carlesso, Renan Giacomelli, Thomas Krause, Andrey Molotnikov, Dietmar Koch, Stephen Kroll, Kamen Tushtev, Yuri Estrin & Kurosch Rezwan. (2013) Improvement of sound absorption and flexural compliance of porous alumina-mullite ceramics by engineering the microstructure and segmentation into topologically interlocked blocks. Journal of the European Ceramic Society 33:13-14, pages 2549-2558.
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M. Dugué, M. Fivel, Y. Bréchet & R. Dendievel. (2013) Indentation of interlocked assemblies: 3D discrete simulations and experiments. Computational Materials Science 79, pages 591-598.
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Arcady Dyskin, Elena Pasternak & Yuri Estrin. 2013. PRICM. PRICM 1525 1534 .
Z.X. Zhang & Q.H. Lei. (2013) Object-oriented modeling for three-dimensional multi-block systems. Computers and Geotechnics 48, pages 208-227.
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Arcady Dyskin, Elena Pasternak & Yuri Estrin. 2016. Proceedings of the 8th Pacific Rim International Congress on Advanced Materials and Processing. Proceedings of the 8th Pacific Rim International Congress on Advanced Materials and Processing 1525 1534 .
S. Khandelwal, T. Siegmund, R.J. Cipra & J.S. Bolton. (2012) Transverse loading of cellular topologically interlocked materials. International Journal of Solids and Structures 49:18, pages 2394-2403.
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Arcady V. Dyskin, Elena Pasternak & Yuri Estrin. (2012) Mortarless structures based on topological interlocking. Frontiers of Structural and Civil Engineering.
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M. Carlesso, A. Molotnikov, T. Krause, K. Tushtev, S. Kroll, K. Rezwan & Y. Estrin. (2012) Enhancement of sound absorption properties using topologically interlocked elements. Scripta Materialia 66:7, pages 483-486.
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Adam Mather, Raymond Cipra & Thomas Siegmund. (2012) Structural integrity during remanufacture of a topologically interlocked material. International Journal of Structural Integrity 3:1, pages 61-78.
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Y. Estrin, A.V. Dyskin & E. Pasternak. (2011) Topological interlocking as a material design concept. Materials Science and Engineering: C 31:6, pages 1189-1194.
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Michael F. Ashby. 2011. Materials Selection in Mechanical Design. Materials Selection in Mechanical Design 299 340 .
J.N. BaucomJ.P. Thomas, W.R. PogueIIIIII & M.A. Siddiq Qidwai. (2010) Tiled Composite Laminates. Journal of Composite Materials 44:26, pages 3115-3132.
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Stephan Schaare, Werner Riehemann & Yuri Estrin. (2009) Damping properties of an assembly of topologically interlocked cubes. Materials Science and Engineering: A 521-522, pages 380-383.
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Yuri Estrin, Arcady Dyskin, Elena Pasternak & Stephan Schaare. (2011) Topological Interlocking in Design of Structures and Materials. MRS Proceedings 1188.
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Charles Brugger, Marc C. Fivel & Yves Bréchet. (2011) Numerical Simulations of Topologically Interlocked Materials Coupling DEM Methods and FEM Calculations: Comparison with Indentation Experiments. MRS Proceedings 1188.
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S. Schaare, A.V. Dyskin, Y. Estrin, S. Arndt, E. Pasternak & A. Kanel-Belov. (2008) Point loading of assemblies of interlocked cube-shaped elements. International Journal of Engineering Science 46:12, pages 1228-1238.
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O. Bouaziz, Y. Bréchet & J. D. Embury. (2008) Heterogeneous and Architectured Materials: A Possible Strategy for Design of Structural Materials. Advanced Engineering Materials 10:1-2, pages 24-36.
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A. Autruffe, F. Pelloux, C. Brugger, P. Duval, Y. Bréchet & M. Fivel. (2007) Indentation Behaviour of Interlocked Structures Made of Ice: Influence of the Friction Coefficient. Advanced Engineering Materials 9:8, pages 664-666.
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A.V. Dyskin, Y. Estrin, E. Pasternak, H.C. Khor & A.J. Kanel-Belov. (2005) The principle of topological interlocking in extraterrestrial construction. Acta Astronautica 57:1, pages 10-21.
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A.V. Dyskin, Y. Estrin, A.J. Kanel-Belov & E. Pasternak. (2003) Interlocking properties of buckyballs. Physics Letters A 319:3-4, pages 373-378.
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M.F. Ashby & Y.J.M. Bréchet. (2003) Designing hybrid materials. Acta Materialia 51:19, pages 5801-5821.
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