Acoustic Metamaterials Based on Local Resonances: Homogenization, Optimization and Applications

Cosmo, Fabio Di; Laudato, Marco; Spagnuolo, Mario

doi:10.1007/978-3-319-72440-9_12

Cited by 41 publications

(22 citation statements)

References 135 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…auxetic, negative stiffness, highly compliant, strongly nonlinear, multistable, etc. This is the motif of the emerging field of (mechanical) metamaterials [35,36].…”

Section: Introductionmentioning

confidence: 85%

Pantographic beam: a complete second gradient 1D-continuum in plane

Barchiesi

Eugster

Placidi

et al. 2019

Z. Angew. Math. Phys.

View full text Add to dashboard Cite

There is a class of planar 1D-continua which can be described exclusively by their placement functions which in turn are curves in a two-dimensional space. In contrast to the Elastica for which the deformation energy depends on the projection of the second gradient to the normal vector of the placement function, i.e. the material curvature, the proposed continuum does also depend on the projection onto the tangent vector, introduced as the stretch gradient. Thus, the deformation energy takes into account the complete second gradient of the placement function. In such a model, nonstandard boundary conditions and more generalized forces such as double forces do appear. The deformation energy of the continuum is obtained by applying a heuristic homogenization procedure to a family of slender discrete pantographic structures constituted by extensional and rotational springs. Within the homogenization process, the overall length of the system is kept fixed, the number of the periodically appearing subsystems , called cells, is increased, and the stiffnesses are appropriately scaled. For two examples, we numerically compare the family of discrete systems with the continuum. The analysis shows that the continuum represents the behaviour of the discrete system already for a relatively moderate number of cells. In particular, the behaviour of the deformation energy error between the discrete and the continuum models when the number of cells tends to infinity is determined by the homogenization process.

show abstract

“…auxetic, negative stiffness, highly compliant, strongly nonlinear, multistable, etc. This is the motif of the emerging field of (mechanical) metamaterials [35,36].…”

Section: Introductionmentioning

confidence: 85%

Pantographic beam: a complete second gradient 1D-continuum in plane

Barchiesi

Eugster

Placidi

et al. 2019

Z. Angew. Math. Phys.

View full text Add to dashboard Cite

show abstract

“…Finally, it would be interesting to study the dynamics in pantographic structures of the same dimensions as those presented in this article. In fact, the propagation of waves in generalized continua [64][65][66] is a non-trivial problem and can lead to unexpected results. Some preliminary results in the field of pantographic structures can be found in [67,68].…”

Section: Discussionmentioning

confidence: 99%

Parametric Experimentation on Pantographic Unit Cells Reveals Local Extremum Configuration

et al. 2019

View full text Add to dashboard Cite

Pantographic metamaterials are known for their ability to have large deformation while remaining in the elastic regime. We have performed a set of experiments on 3D printed pantographic unit cells to parametrically investigate their response when undergoing tensile, compression, and shear loading with the aim of i) studying the role of each parameter in the resultant mechanical behavior of the sample, and ii) providing a benchmark for the mathematical models developed to describe pantographic structures. Results show the existence of local extrema in the space of the geometrical parameters, suggesting the use of optimization techniques to find optimal geometrical parameters resulting in desired functionalities. We have also performed tensile relaxation tests on the samples, with the results indicating the complexity of the dynamic behavior and the existence of multiple relaxation characteristic times. Such results can be used to for calibrating mathematical models describing pantographic structures under dynamic loadings.

show abstract

“…By substituting the results (22) into (20), a kinematic reduction is performed resulting in the deformation energy functional of the pantographic beam…”

Section: Preliminariesmentioning

confidence: 99%

Large in-plane elastic deformations of bi-pantographic fabrics: asymptotic homogenization and experimental validation

Barchiesi

Eugster

Dell’Isola

et al. 2019

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

Bi-pantographic fabrics are composed of two families of pantographic beams and correspond to a class of architectured materials that are described in plane as second-gradient 2D-continua. On a discrete level, a pantographic beam is a periodic arrangement of cells and looks like an expanding barrier. The materialisation of a bi-pantographic fabrics made by Polyamide was achieved by additive manufacturing techniques. Starting from a discrete spring system, the deformation energy of the corresponding continuum is derived for large strains by asymptotic homogenisation. The obtained energy depends on the second gradient of the deformation through the rate of change in orientation and stretch of material lines directed along the pantographic beams. Displacementcontrolled bias extension tests were performed on rectangular prototypes for total elastic extension up to 25%.Force-displacement measurements complemented by local digital image correlation analyses were used to t the continuum model achieving excellent agreement.

show abstract

Acoustic Metamaterials Based on Local Resonances: Homogenization, Optimization and Applications

Cited by 41 publications

References 135 publications

Pantographic beam: a complete second gradient 1D-continuum in plane

Pantographic beam: a complete second gradient 1D-continuum in plane

Parametric Experimentation on Pantographic Unit Cells Reveals Local Extremum Configuration

Large in-plane elastic deformations of bi-pantographic fabrics: asymptotic homogenization and experimental validation

Contact Info

Product

Resources

About