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Book Review---First book on "Dynamics of Lattice Materials”---by Srikantha Phani and Mahmoud Hussein

Pradeep Sharma's picture

“Metamaterials” are the fabled materials exhibiting properties and functionalities that defy expectations. Or at least that's how I have always defined them to myself. These first emerged on the scientific scene in the nineties; or perhaps that is when an extensive flurry of activities on this subject can be traced to. The initial focus was on designing (what appeared to me as) composites with a specific geometrical inner structure that allowed the emergence of electromagnetic properties not typically seen in nature; such as negative refractive index. An experimental demonstration of a partial invisibility cloak for microwave radiation using metamaterials was realized in 2006 and generated much attention. Negative index materials may lead to the creation of a “super-lens”----a lens that possesses a resolution beyond the so-called diffraction limit thus circumventing the limits of conventional optical microscopy.

Over the past two decades, this research field has rapidly grown and diversified beyond the manipulation of electromagnetic waves. Acoustic and elastic waves in deformable media have given rise to mechanical metamaterials that purport to control elastic and sound waves, typically utilizing the presence of local resonators either inserted or attached to a host medium. Aside from acoustic/elastic cloaking, applications are expected in medical diagnostics, noise and vibration reduction, sound absorption, flow control, and others. This is where mechanics has most directly intersected with metamaterials although the field continues to be redefined and expanded[1].

Intimately connected to metamaterials is the broader, and also emerging, field of phononics‒which in principle encompasses acoustic/elastic metamaterials, in addition to what is known as phononic crystals. These crystals are periodic materials with carefully tuned wave dispersion characteristics based on interference mechanisms rather than local resonances.

Noting a surge of activity on this topic in mechanics, especially viewed through the vantage point of some of my editorial responsibilities, I have keenly followed the progress of this field; more perhaps as an interested non-specialist than as a practioner. I have had an eye out for possible pedagogical and tutorial resources and am happy to note a new addition on that front.  Professors Srikantha Phani, from the University of British Columbia, and Mahmoud Hussein from the University of Colorado Boulder have edited a new book: Dynamics of Lattice Materials[2]. In essence, in this book, the authors address a special (and perhaps common) class of periodic materials that resemble a structural version of a crystal. In lattice materials, each unit cell motif can be repeated to obtain a macroscopic structure with bespoke unique or emergent properties. As a sub-category of phononic materials, lattice materials typically exhibit relatively high porosity to reduce weight. In the age of 3D printing, lattice materials are especially attractive and even a die-hard theoretician like I, with two left thumbs, have recently fabricated a prototype to test out some ideas!

Both the editors are mechanicians with a special interest in elastodynamics, and this is reflected in the tone and selection of the chapters. The book appears to be designed to encourage newcomers to this field, especially those from the mechanics community. The twelve chapters of the book feature several key researchers on this topic such as Professors Katia Bertoldi, Wesley Cantwell, Gregory Hulbert, Michael Leamy, Andrew Norris, Damiano Pasini, Massimo Ruzzene, Craig Steeves, Cetin Yilmaz, among others.  I note that of the twelve chapters, five of them feature one of the two editors and this perhaps has the positive outcome that despite being an edited book, the content flows very naturally and coherently without the disjointedness sometimes evident in edited books. Also very attractive is that the book starts with a 9-page foreword written by Professor Graeme Milton[3], a pioneer in the mathematical theory of composites and metamaterials.

The first three chapters of the books provide a broad introduction to the subject and I would encourage everyone to read these. The remaining nine chapters can be read based on individual interest. Chapter 1 (authored by the editors, Professors Phani and Hussein), Introduction to Lattice Materials, provides an overview of the subject and a guideline to the book itself. In Chapter 2, Pasini and Arabnejad introduce Elastostatics of Lattice Materials which also provides some essential background material for some of the concepts on dynamics introduced in later chapters. In Chapter 3, Professor Phani provides an inspired tutorial on Elastodyamics of Lattice Materials. Building on the foundations set by the first three chapters, the remaining ones tackle topics such as Wave Propagation in Damped or Nonlinear Lattice Materials, Stability of Lattice Materials, Pentamodes and Local Resonances, Nanolattices, and several others.

In addition to the first three chapters, I read four others that I had an interest in. This is a very well-written book overall and I congratulate all the authors for striking an excellent balance between being gentle and pedagogical enough to engage newcomers to the field and comprehensive enough to provide a state-of-the-art review on topics of contemporary interest.  Perhaps the only thing missing, in my opinion, is a “closure” chapter that tries to summarize the key challenges and open issues in this field in a single location[4].  That would be a welcome addition to the second edition.


[1] The reader may wish to also check out the iMechanica Journal Club issue authored by Professor Hussein.

[2] This book is published by Wiley and is readily available on amazon.

[3] I recently also reviewed a book by Graeme Milton on the topic of composites. Several aspects of his recent research as well as his new book touch upon metamaterials.

[4] There is a discussion of open issues in the book but those usually appear contextually and are spread across the various chapters.


azadpoor's picture

Hello Pardeep and thank you for this nice review of the book. As you know, many researchers have started to use the term metamaterials when referring to architectured materials that are designed to exhibit rare or unprecedented quasi-static mechanical properties (e.g. negative Poisson's ratio, negative compressibility, negative stiffness, ultra-high properties, etc) [1-6]. Shape morphing “materials” and (reconfigurable) materials with tunable properties are also sometimes called metamaterials [7-11]. I have recently coined the term meta-biomaterials to refer to architectured materials that are designed to exhibit an unusual and highly favorable combination of mechanical properties, mass transport properties, and geometrical features (e.g. curvature), leading to superior biological performance such as improved tissue regeneration [12-15]. I thought this might be a worthwhile addition to your nice overview of metamaterials.

1. Eidini, M. and G.H. Paulino, Unraveling metamaterial properties in zigzag-base folded sheets. Science advances, 2015. 1(8): p. e1500224.

2. Kolken, H.M. and A. Zadpoor, Auxetic mechanical metamaterials. RSC Advances, 2017. 7(9): p. 5111-5129.

3. Lee, J.H., J.P. Singer, and E.L. Thomas, Micro‐/nanostructured mechanical metamaterials. Advanced materials, 2012. 24(36): p. 4782-4810.

4. Yasuda, H. and J. Yang, Reentrant origami-based metamaterials with negative Poisson’s ratio and bistability. Physical review letters, 2015. 114(18): p. 185502.

5. Zadpoor, A.A., Mechanical meta-materials. Materials Horizons, 2016. 3(5): p. 371-381.

6. Zheng, X., et al., Ultralight, ultrastiff mechanical metamaterials. Science, 2014. 344(6190): p. 1373-1377.

7. Grima, J.N., et al., Smart metamaterials with tunable auxetic and other properties. Smart Materials and Structures, 2013. 22(8): p. 084016.

8. Lv, C., et al., Origami based mechanical metamaterials. Scientific reports, 2014. 4.

9. Neville, R.M., F. Scarpa, and A. Pirrera, Shape morphing Kirigami mechanical metamaterials. Scientific reports, 2016. 6: p. 31067.

10. Silverberg, J.L., et al., Using origami design principles to fold reprogrammable mechanical metamaterials. science, 2014. 345(6197): p. 647-650.

11. Tang, Y., et al., Design of hierarchically cut hinges for highly stretchable and reconfigurable metamaterials with enhanced strength. Advanced Materials, 2015. 27(44): p. 7181-7190.

12. Ahmadi, S., et al., Fatigue performance of additively manufactured meta-biomaterials: The effects of topology and material type. Acta Biomaterialia, 2017.

13. Bobbert, F., et al., Additively manufactured metallic porous biomaterials based on minimal surfaces: A unique combination of topological, mechanical, and mass transport properties. Acta Biomaterialia, 2017. 53: p. 572-584.

14. Yavari, S.A., et al., Relationship between unit cell type and porosity and the fatigue behavior of selective laser melted meta-biomaterials. Journal of the mechanical behavior of biomedical materials, 2015. 43: p. 91-100.

15. Zadpoor, A.A., Design for Additive Bio-Manufacturing: From Patient-Specific Medical Devices to Rationally Designed Meta-Biomaterials. International Journal of Molecular Sciences, 2017. 18(8): p. 1607.

Pradeep Sharma's picture

Thanks for your comment. Yes, while initially, the word "metamaterials" was coined to describe a very specific class of materials with emergent properties related to electromagnetism, this field has evolved considerably and now encompasses so much more. You have given a good list. On a personal note, I have always understood metamaterials to simply mean a generalized composite that is engineered to exhibit properties that are in some sense considered unusual.

azadpoor's picture

Yes, I agree that the most important point is to have unusual properties. The concept of comoposite is also universally applicable as long as we consider "void" also a phase of the composite!

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