Architectured materials and mechanical metamaterials are an emerging and exciting class of materials with the promise of advantageous performance and multifunctional properties. These materials are characterized by specific and periodic structural features which are larger than what is typically considered a microstructural length scale (such as a grain size) but smaller than the size of the final component made of the architectured material. This class of materials includes but is not limited to lattice materials and cellular material systems, dense material systems composed of building blocks of well-defined size and shape.
We recently organized an International Union of Theoretical and Applied Mechanics (IUTAM) symposium dedicated to “Architectured Material Mechanics” in Chicago, IL (USA), Sept. 17–19, 2018. This event provided a review of the state of the art and a platform for discussions on the future of the science and engineering of architectured materials. It covered the mechanics, design, fabrication, and mechanical performance of all categories of architectured materials including lattice materials, metamaterials, multilayered system, and topologically interlocked materials. The 89 researchers who attended the symposium came from 18 countries: Austria, Canada, China, Denmark, France, Germany, Israel, Poland, Argentina, China, Korea, Switzerland, The Netherlands, Spain, Sweden, Switzerland, United Arab Emirates, and United States. A wide range of disciplines was represented including Physics, Architecture, Computer Science, Materials, Civil, Materials and Mechanical Engineering. The symposium also demonstrated the enthusiasm of young researchers active in research on this topic as 32 participants were either graduate students or postdoctoral researchers. Abstracts of all conference contributions are available at Ref. [1].
This special issue of the Journal of Applied Mechanics provides expanded contributions of the three original conference themes: (1) design, optimization, and fabrication; (2) bioinspiration, strength, and toughness; and (3) heterogeneity, instability, shape transformation, and dynamical behavior.
Design, optimization, and fabrication: Sessions on this theme included discussion on topics of topology optimization; periodic truss structures; origami materials; active architecture materials; knit-process materials; macro-, micro-, and nanoscale concepts; and on material assembly concepts. In this special issue, Tessmann and Rossi contrast features of monolithic and segmented architecture material systems and structures and demonstrate the vast design space envisioned for material systems by the assembly of unit building blocks. Along similar lines, Frederickson describes the specific work of the architect Ernest Irving Freese and underpins his tile structures with computational geometry. Both contributions challenge researchers in the field to expand their views on possible material systems’ configurations. Kontsos et al. and Picu et al. [2] demonstrate material architecture in fibrous materials. Kontsos et al. demonstrate the material property of knit-process-derived material systems. The underlying manufacturing processes allow for the realization of various periodic material architectures and mechanical response features. Deogekar et al. [2], on the other hand, discuss fiber materials with random space associated with Voronoi construction principles. This contribution indicates opportunities to tune a linear versus nonlinear material response. Dirrenberger et al. consider periodic lattice structures and systematically explore a parametric geometry space, thereby deriving architecture–property relationships for auxetic response. Finally, Reasa and Lakes present a design of a lattice material with chiral elements, with uncommon properties in terms of twist-compression coupling and size effects.
Bioinspiration, strength, and toughness: Sessions on this theme focused on achieving novel material configurations such as nacre architecture, interlocked geometries, auxetics, and lattice configurations, all with exceptional toughness and new underlying mechanics principles. Speakers discussed applications in biomedical devices and in material systems for impact protection. In this special issue, several papers show how material architecture provides new opportunities to achieve increased strength and toughness. Barthelat et al. and Siegmund et al. demonstrate how tessellated material systems (also found in many biological systems) can produce remarkable mechanical performance. In these materials, the interaction of individual building blocks together with the respective contact and interface interactions leads to the overall material system response. Barthelat et al. used a computational mechanics approach to capture the increase in strength and toughness achievable for tessellated material assemblies under in-plane loading. Siegmund et al. [9] derived closed form expressions for plate-like material systems based on geometrically interlocked building blocks. Kolednik et al. show how soft interlayers with regular spacing can increase toughness by way of a material homogeneities effect. Mohr et al. provide a study on the relationship between stiffness and strength and the cellular structure of honeycomb-like materials and compare the classical hexagon and triangular lattices to a class of lattices architectures with chiral character. These authors demonstrate how the added architecture feature of chirality allows to not only tailor stiffness and strength but also Poisson’s ratio.
Heterogeneity, instability, shape transformation, and dynamical behavior: The symposium sessions in this theme focused on topics of wave propagation and band gaps, phase transformation and instabilities, on active material concepts, and the issue of nonreciprocity in architecture materials. Pasini et al. show how material architecture and hierarchy can be used to amplify local thermal expansion and generate large, anisotropic change of shape. Zavattieri et al. explore the mechanics of phase transforming cellular materials based on chiral architectures, using tape springs as the base material. They show how the interplay of the base elements (tape springs) and the architecture can lead to superior energy dissipation. Coulais et al. explore another route for energy dissipation, where the intrinsic viscoelasticity of 3D printed rubbers can be harnessed through snapping mechanisms to generate high damping for vibration and impact applications. Vibrations and stress can also be manipulated with architecture as demonstrated in the paper by Matlack et al. In particular, they show how signal attenuation near band gaps can be tuned with the lattice architecture of the material. Finally, the dynamic response of architectured materials can also be controlled with phenomena involving multiple physics as demonstrated by Rudykh et al. who study wave band gaps appearing in magnetoactive laminates.
The field of architectured materials and metamaterial is a fast evolving and exciting area of research, and we hope that this special issue will give you a good overview of the recent accomplishments and potential for the type of material. We also hope that you enjoy reading this special issue, as much as enjoyed putting it together.
Acknowledgment
The symposium was supported in part by a conference grant from IUTAM (Funder ID: 10.13039/501100011865)—the International Union of Theoretical and Applied Mechanics—and by a grant from the National Science Foundation (Award #1820220; Funder ID: 10.13039/501100008982).
Appendix: Symposium Program
Oral Presentations
Focus 1: Design, optimization, and fabrication
Yves Brechet: Architectured Materials: 15 Years of Progress, and Emerging Challenges
Ole Sigmund and Jeroen Groen: Extremal Material and Structure Design by Topology Optimization
Heinrich M. Jaeger, Kieran A. Murphy, and Leah K. Roth: Architectured Particulate Materials
Frank Zok, Matthew R. Begley, and Ryan M. Latture: Design and Performance of Periodic Trusses
Julian J. Rimoli, Hossein Salahshoor, and Raj Kumar Pal: Topology Matters: Expanding the Design Space of Lightweight Mechanical Metamaterials
Rafael Estevez, Alexis Faure, Georgios Michailidis, Charles Dapogny, and Grégoire Allaire: Shape and Topology Optimization of Architectured Materials: From the Design to Real Structures
Antonios Kontsos: The Behavior of Knitted Textiles Through the Lens of Architectured Material Mechanics
Greg N. Frederickson: Hidden in Plane Sight: The Extraordinary Vision of Ernest Irving Freese
Julia R. Greer, Lucas Meza, Arturo Mateos, Carlos Portela, Dennis Kochmann, and Yong-Wei Zhang: Mechanics of Three-Dimensional Nano-Architected Meta-Materials
Yonggang Huang: Mechanics-Guided Deterministic 3D Assembly
SungWoo Nam: Mechanical Instability-Driven Architecturing of Atomically-Thin Materials
Jie Yin: Kirigami-Based Mechanical Metamaterials
Andres F. Arrieta, Jakob Faber, Katherine S. Riley, and André R. Studart: Extending Origami: Crease Pre-stressing for Functional Adaptation
A. Mocci, D. Codony, A. Abdollahi, and I. Arias: Flexoelectricity-Based Electromechanical Metamaterials
Kunal Masania and André Stuart: 3D Printing of Biologically-Inspired Materials
Focus 2: Bioinspiration, strength, and toughness
Zdeněk P. Bažant and Wen Luo: Fishnet Statistics for Failure Probability of Nacreous Staggered Laminar Materials
Francois Barthelat: Exploring Material Property Space Using Bioinspiration and Architecture
H. Daniel Wagner, Israel Greenfeld, Wenyong Zhang, and XiaoMeng Sui: Intermittent Interfaces: Bioinspired Strategies Towards Material Resilience
Iwona Jasiuk, Fereshteh A. Sabet, Christopher Kozuch, Diab Abueidda, Frances Su, and Joanna McKittrick: Bioinspired Architectured Materials With Interpenetrating Phases
Sung Hoon Kang, Galip Ozan Erol, Emilio Bachtiar, and Azra Horowitz: Architected Cardiovascular Implants for Accommodating Growth
Nan Hu, Hanqing Zhang, Daobo Zhang, Peng Feng, Amal Jerald Joseph M, and Davut B. Gul: Tunable Failure in Non-periodic Architected Materials Inspired by Physarum Polycephalum Growth
Stavros Gaitanaros: Random Foams: Instabilities, Fracture, and Shocks
Oliver Tessmann and Andrea Rossi: Parametric and Combinatorial Topological Interlocking Assemblies
Thomas Siegmund: Topologically Interlocked Material Systems: From a Material Design Concept to Properties
Catalin R. Picu and Anirban Pal: Interlocked Fragmented Continua: A Stochastic Metamaterial
Thomas Tancogne-Dejean, Marianna Diamantopoulou, Colin Bonatti, Maysam Gorji, and Dirk Mohr: Plastic Anisotropy of Elastically-Isotropic Beam, Shell and Plate Networks: Theory and Experiments
Tiantian Li and Lifeng Wang: Exploiting Auxetics to Design Composite Materials With Enhanced Mechanical Performance
Frédéric Albertini, Justin Dirrenberger, Andrey Molotnikov, and Cyrille Sollogoub: Mechanical Behaviour of Architectured Auxetic Hybrid Lattice Structures
Focus 3: Heterogeneity, instability, shape transformation, and dynamical behavior
Rod Lakes: Extreme Classical and Nonclassical Physical Properties in Heterogeneous Materials
Otmar Kolednik, Roland Kasberger, and Masoud Sistaninia: Design of Damage-Tolerant and Fracture-Resistant Materials by Utilizing the Material Inhomogeneity Effect
Gerold A. Schneider, Berta Domènech, Diletta Giuntini, and Büsra Bor: Organically Linked Nanoparticles as Building Blocks for Architectured Materials
C. Ayas, W. E. D. Nelissen, and C. Tekoglu: 2D Lattice Materials for Low Energy Actuation
Corentin Coulais: Non-reciprocity in Mechanical Metamaterials
Amr Farag, Hang Xu, and Damiano Pasini: Thermally Actuated Planar Lattices With High Fractal Stiffness
Yanyu Chen: 3D Printed Hierarchical Honeycombs With Shape Integrity Under Large Compressive Deformations
Katia Bertoldi: Architected Materials: From Reconfigurability to Nonlinear Waves
Pablo D. Zavattieri, Yunlan Zhang, Miriam Velay, David Restrepo, and Nilesh D. Mankame: Architecting Stress- and Temperature-Induced Phase Transformation
Stephan Rudykh, Viacheslav Slesarenko, Pavel Galich, and Jian Li: Micromechanics and Instabilities of Soft Architectured Composite Materials
Kathryn H. Matlack, and Ignacio Arretche: Dynamic and Mechanical Properties of Lattice-Resonator Meta-Structures
G. L. Huang: Wave Propagation in Modulated Phononic Crystals and Metamaterials
Kuo-Chih Chuang, Xiang Fang, and Zhiwen Yuan: Forming Flexural Band Gaps of Phononic Crystal Beams Based on Concentrated Masses
A. Srikantha Phani: Vibroacoustic Response of Lattices: Opportunities and Challenges
Jaejong Park and Alok Sutradhar: Design of Tunable Architectured Metamaterials for Biomedical Applications
Poster Contributions
Bill Arrighi, Jun Kudo, Dan Tortorelli, Seth Watts, and Dan White: Three-Dimensional Multiscale Design Using Neural Net Surrogate Models of Lattice Material Response
Kieran A. Murphy, and Heinrich M. Jaeger: Designed to Fail: Granular Plasticity and Particle Shape
Vince Vernacchio and Thomas Siegmund: Lattice Structures and Strength Optimization
Diab W. Abueidda, Iwona Jasiuk, and Nahil A. Sobh: Acoustic Band Gaps, Sound Attenuation, and Elastic Stiffness of PMMA Cellular Materials Based on Triply Periodic Minimal Surfaces
Sree Kalyan Patiballa and Girish Krishnan: Conceptual Design of Spatial Auxetic Microstructures
M. S. Hosseini, S. N. Garner, S. E. Naleway, J. M. McKittrick, and P. D. Zavattieri: Role of Architecture in Controlling Crack Propagation Direction Bio-Inspired From Boxfish Scute
Will Langford and Neil Gershenfeld: Discretely Assembled Compliant Mechanisms
Susanta Ghosh, Mark Coldran, Praveen Bulusu, Upendra Yadav, and Trisha Sain: Mechanics of Micro-Architectured Glass: Inverse Identification of Interface Properties and a Novel Analytical Model
Thomas Tancogne-Dejean and Dirk Mohr: BCC Metamaterials Composed of Tapered Beams: Stiffness and Energy Absorption
Aman Thakkar, Nilesh Mankame, Pablo Zavattieri, and Andres F. Arrieta: Energy Harvesting in Phase Transforming Materials
H. Cui, M. R. O’Masta, V. S. Deshpande, and Xiaoyu (Rayne) Zheng: Fracture Toughness of Hierarchical, Low Density Architected Metamaterials
Yunlan Zhang, Kristiaan Hector, Mirian Velay-Lizancos, David Restrepo, Nilesh D. Mankame, and Pablo Zavattieri: Mechanics of Energy Absorbing Phase Transforming Cellular Materials
Di Wang, Alireza Zaheri, Benjamin Russell, Pablo Zavattieri, and Horacio Espinosa: Fiber Reorientation Behavior of Bioinspired Bouligand Architectures With Functional Graded Fiber Orientation
Myungwon Hwang and Andres F. Arrieta: Input-Independent Response-Invariant Wave Propagation in Bistable Lattices With Elastic Interactions
Carlos M. Portela, Dennis M. Kochmann, and Julia R. Greer: Controlling the Effect of Nodes on the Mechanical Response of Lattice Architectures
Muhammed Imam, Trisha Sain, and Julien Meaud: Computational Design of Architectured Materials With Hierarchical Interlocking for Improved Multifunctional Properties
Andres Bejarano and Christoph Hoffmann: Topological Interlocking Cylinder Configurations: A Geometric Approach
Miroslawa El Fray, Rahul Sahay, XiaoMeng Sui, and H. Daniel Wagner: Architectured Helically Coiled Structures Through Novel Electro-Writing Technique
Hang Xu, Amr Farag, and Damiano Pasini: Routes to Program Thermal Expansion in Three-Dimensional Lattices Built From Tetrahedral Building Blocks
Pu Zhang: Symmetry of Phonon Modes for Periodic Structures With Glide Symmetry
Baig Al-Muhit and Florence Sanchez: Mechanical Properties of Nanolaminate Tobermorite-9 Å/Graphene Composite
Lichen Fang, Jing Li, Zeyu Zhu, Santiago Orrego, and Sung Hoon Kang: Piezoelectric Polymer Thin Films With Architected Cuts
Haodong Du, Liang Zhang, Bo Peng, and Wenbin Yu: Constitutive Modelling of Cosserat Metamaterials
Xiao Shan, Lu Liu, Ahmad Rafsanjani, and Damiano Pasini: Durable Bistable Auxetics Made of Rigid Solids
Mohammad Mirkhalaf, Tao Zhou, Florent Hannard, and Francois Barthelat: Strong and Tough Ceramics Using Architecture and Topological Interlocking
Qianli Chen and Ahmed Elbanna: Emergent Wave Phenomena in Coupled Elastic Bars: From Extreme Attenuation to Realization of Elastodynamic Switches
J. William Pro, Najmul Abid, Ali Shafiei, and Francois Barthelat: Discrete Element Models of Architectured Biological and Bio-inspired Composites
Marianna Diamantopoulou, Colin Bonatti, and Dirk Mohr: Periodic Ceramic-Polymer Shell-Network of High Specific Stiffness
Mirit Sharabi and H. Daniel Wagner: Bio-mimetics of Structural Micro-Mechanisms in Soft Composite Materials
Howon Lee, Chen Yang, and Manish Boorugu: Lightweight Microlattice With Tunable Mechanical Properties Using 3D Printed Shape Memory Polymer
Michael Jandron and David Henann: A Numerical Simulation Capability for Electroelastic Wave Propagation in Dielectric Elastomer Composites: Application to Tunable Soft Phononic Crystals
Ye-eun Na, Dahye Shin, Kisun Kim, Seokwoo Jeon, and Dongchan Jang: Emergence of New Density-Strength Scaling Law in 3D Hollow Ceramic Nano-Architectures
Andrew Williams and Thomas Siegmund: Tesselations and Percolations in Topologically Interlocked Stereotomic Material Systems
Colin Bonatti and Dirk Mohr: Mechanical Response of Three Cubic Shell-Based Metamaterials
Amrita Kataruka and Shelby B. Hutchens: Analysis of Plant-Inspired, Osmosis-Mediated Structures
Vanessa Restrepo, Miriam Velay, and Pablo Zavattieri: Structural Interfaces Bioinspired by Natural Adhesives: New Self-Healing Material With High Energy Dissipation
Catalin R. Picu: Architected Fibrous Networks With Highly Tuneable Properties
Christine E. Gregg, Benjamin Jenett, and Kenneth C. Cheung: Assembled Composite Lattice Structures: Towards Ideal Performance in Large-Scale Applications
Le Cao: Multiscale Method in Lattice Structures Stability Analysis With Topology Optimization
Caglar Oskay and Ruize Hu: Multiscale Simulation Framework for Transient Wave Propagation in Viscoelastic Composites
Davis J. McGregor, Sameh Tawfick, and William P. King: Mechanical Properties of Hexagonal Lattice Structures Fabricated Using Continuous Liquid Interface Production Additive Manufacturing
Josh Pribe and Thomas Siegmund: Architecture and Internal Material Length Scale: Fatigue Crack Growth Across Weak Interfaces
Kamran Khan: Architected Active Metamaterials
