A General Concept of Dynamic Materials

Lurie, Konstantin A.

doi:10.1007/0-387-38280-1_1

Cited by 3 publications

(9 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This change is governed by a controller. A composite assembled from such materials becomes a dynamic composite, see [26,27,76].…”

Section: Optimization Of Dynamic Materialsmentioning

confidence: 99%

“…A double period is a unit square divided in four quadrants. The first and the third quadrants are occupied by the fast material (v2) and the second and the fourth by the slow material (v1) [27,28]. This construction results in the checkerboard material assembly in space–time.…”

Section: Optimization Of Dynamic Materialsmentioning

confidence: 99%

“…Below, we illustrate the results of numerical analysis described in [27–29]. In figure 4 a , there are boldface and dashed lines.…”

Section: Optimization Of Dynamic Materialsmentioning

confidence: 99%

“…Another feature of the energy concentrating structure is that the wave routes never intersect; instead, are densely compressed and tend to the stable periodic limit circles. Accordingly, the energy is accumulated in the array of progressively sharpening pulses, figure 4 a (limit cycles in the corresponding phase space) composed from densely compressed wave routes, see [27,28]. Remarkably, such constructions need no more than Snell’s Law plus the analysis of kinematics of the wave routes that merge towards each other to be compressed in pulses as time evolves.…”

Section: Optimization Of Dynamic Materialsmentioning

confidence: 99%

“…[26,28,29,35,69]. The introduction to the theory of optimal DM was presented in the book [27]. This theory received further development in the papers [23,25,30–34], among others.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Optimal structures for focusing and energy accumulation: mathematical models and intuition

Cherkaev,

Lurie

2023

Proc. R. Soc. A.

View full text Add to dashboard Cite

Metamaterials and composite structures are able to manipulate waves and focus fields and currents in desirable directions. Designs based on spatial and temporal variation of material properties create structures forcing fluxes into specified parts of the domain or concentrating energy into arrays of progressively sharpening pulses. The paper discusses examples of focusing structures, mathematical and intuitive considerations that influence optimal design theory. The optimality requirement introduces zones of optimal composites with variable microgeometry. The observed absence of classical solutions motivates the extension of the class of optimal partitions to composites. Such materials also provide a solution to the problem of optimal design of a thermal lens focusing thermal fluxes when the incoming fluxes are not completely known in advance. An extension of designs to dynamical materials such as space–time checkerboard composites introduces metamaterials with additional capabilities that control the accumulation of energy in the propagating waves. The discussed mathematical methods of focusing and suitable properties alternation targeted on optimality are illustrated by physical examples.

show abstract

“…This change is governed by a controller. A composite assembled from such materials becomes a dynamic composite, see [26,27,76].…”

Section: Optimization Of Dynamic Materialsmentioning

confidence: 99%

Section: Optimization Of Dynamic Materialsmentioning

confidence: 99%

“…Below, we illustrate the results of numerical analysis described in [27–29]. In figure 4 a , there are boldface and dashed lines.…”

Section: Optimization Of Dynamic Materialsmentioning

confidence: 99%

Section: Optimization Of Dynamic Materialsmentioning

confidence: 99%

“…[26,28,29,35,69]. The introduction to the theory of optimal DM was presented in the book [27]. This theory received further development in the papers [23,25,30–34], among others.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Optimal structures for focusing and energy accumulation: mathematical models and intuition

Cherkaev,

Lurie

2023

Proc. R. Soc. A.

View full text Add to dashboard Cite

show abstract

Mechanical metamaterials

2023

View full text Add to dashboard Cite

Mechanical metamaterials, also known as architected materials, are rationally designed composites, aiming at elastic behaviors and effective mechanical properties beyond (“meta”) those of their individual ingredients – qualitatively and/or quantitatively. Due to advances in computational science and manufacturing, this field has progressed considerably throughout the last decade. Here, we review its mathematical basis in the spirit of a tutorial, and summarize the conceptual as well as experimental state-of-the-art. This summary comprises disordered, periodic, quasi-periodic, and graded anisotropic functional architectures, in one, two, and three dimensions, covering length scales ranging from below one micrometer to tens of meters. Examples include extreme ordinary linear elastic behavior from artificial crystals, e.g., auxetics and pentamodes, “negative” effective properties, behavior beyond classical linear elasticity, e.g., arising from local resonances, chirality, beyond-nearest-neighbor interactions, quasi-crystalline mechanical metamaterials, topological band gaps, cloaking based on coordinate transformations and on scattering cancellation, seismic protection, nonlinear and programmable metamaterials, as well as space-time-periodic architectures.

show abstract

High-order homogenization of the time-modulated wave equation: non-reciprocity for a single varying parameter

Touboul,

Lombard,

Assier

et al. 2024

Proc. R. Soc. A.

View full text Add to dashboard Cite

Laminated media with material properties modulated in space and time in the form of travelling waves have long been known to exhibit non-reciprocity. However, when using the method of low-frequency homogenization, it was so far only possible to obtain non-reciprocal effective media when both material properties are modulated in time, in the form of a Willis-coupling (or bi-anisotropy in electromagnetism) model. If only one of the two properties is modulated in time, while the other is kept constant, it was thought impossible for the method of homogenization to recover the expected non-reciprocity since this Willis-coupling coefficient then vanishes. Contrary to this belief, we show that effective media with a single time-modulated parameter are non-reciprocal, provided homogenization is pushed to the second order. This is illustrated by numerical experiments (dispersion diagrams and time-domain simulations) for a bilayered modulated medium.

show abstract

A General Concept of Dynamic Materials

Cited by 3 publications

References 16 publications

Optimal structures for focusing and energy accumulation: mathematical models and intuition

Optimal structures for focusing and energy accumulation: mathematical models and intuition

Mechanical metamaterials

High-order homogenization of the time-modulated wave equation: non-reciprocity for a single varying parameter

Contact Info

Product

Resources

About