Pathway towards Programmable Wave Anisotropy in Cellular Metamaterials

Abstract

In this work, we provide a proof-of-concept experimental demonstration of the wave control capabilities of cellular metamaterials endowed with populations of tunable electromechanical resonators. Each independently tunable resonator comprises a piezoelectric patch and a resistor-inductor shunt, and its resonant frequency can be seamlessly re-programmed without interfering with the cellular structure's default properties. We show that, by strategically placing the resonators in the lattice domain and by deliberately activating only selected subsets of them, chosen to conform to the directional features of the beamed wave response, it is possible to override the inherent wave anisotropy of the cellular medium. The outcome is the establishment of tunable spatial patterns of energy distillation resulting in a non-symmetric correction of the wavefields. INTRODUCTIONCellular solids are porous media known to display unique combinations of complementary mechanical properties, such as high stiffness and high strength at low densities [1]. Lattice materials-cellular solids with ordered architectures-are obtained by spatially tessellating a fundamental building block (unit cell) comprising simple slender structural elements such as beams, plates or shells. Advances in additive manufacturing have recently propelled a resurgence of architected cellular solids as mechanical metamaterials with unprecedented functionalities at multiple scales [2][3][4][5]. Examples include fully-recoverable, energy absorbing lattices with bucklable struts [6,7], pentamode fluid-like materials that behave as "unfeelability" cloaks [8], lattices with negative Poisson's ratio [9], negative thermal expansion [10], and smart lattices with programmable stiffness [11].Lattice structures also display unique dynamic properties. They commonly feature Bragg-type bandgaps as a result of their periodicity and occasionally subwavelength bandgaps for special unit cell designs or in the presence of internal resonators, thus behaving as frequency-selective stop-band filters for acoustic [12], elastic [13][14][15][16][17][18][19] and electromagnetic waves [20]. They also display elastic wave anisotropy, which manifests as pronounced beaming of the energy according to highly directional patterns [13,[21][22][23][24][25][26][27][28][29][30]. This behavior can be attributed to the fact that, at the cell scale, elastic waves are forced to propagate along the often tortuous pathways dictated by the links/struts. The spatial characteristics, symmetry landscape and frequency dependence of the anisotropic patterns are dictated by the unit cell's architecture [31,32] and are usually irreversibly determined during the design and fabrication stages. To endow cellular solids with functional flexibility and active spatial wave management capabilities, we need our structural systems to be tunable or programmable [33][34][35][36][37][38][39][40][41][42]. To ensure that geometry and material requirements imposed by other functional constraints are preserved during the tuning pr...

Foundations for Soft, Smart Matter by Active Mechanical Metamaterials

“…[199] Bergamini et al [200] devised a periodic hybrid metamaterial consisting of elastic beam and collocated piezoelectric elements that, when shunted, provided significant wave at-tenuation at frequencies tuned according to the shunt circuit parameters. Spatial wave control capability is demonstrated by Celli et al [201] in a lattice-resonator network using piezoelectrics and resistor-inductor shunts, Figure 3a. The authors discovered means to override intrinsic anisotropy of wave guiding in the lattice via the selective activation of the electromechanical resonators.…”

“…Adapted with permission. [ 201 ] Copyright 2018, American Physical Society. b) Magnetic field control of soft structures with programmed ferromagnetic domains to obtain complex 3D shape.…”

“…Spatial wave control capability is demonstrated by Celli et al. [ 201 ] in a lattice‐resonator network using piezoelectrics and resistor‐inductor shunts, Figure a. The authors discovered means to override intrinsic anisotropy of wave guiding in the lattice via the selective activation of the electromechanical resonators.…”

“…The authors discovered means to override intrinsic anisotropy of wave guiding in the lattice via the selective activation of the electromechanical resonators. [ 201 ] Piezoelectric material implementations of active mechanical metamaterials benefit from the intrinsic self‐sensing property of piezoelectric structural integrations, [ 202 ] although the brittle nature of piezoelectrics and their high bulk modulus [ 203 ] pose some challenges in the synthesis of soft matter.…”

Distillation of nonlocality in porous solids

“…From the above discussion, it emerges that the VO framework provides a very natural mechanism for the distillation of meaningful nonlocal representations. The above concept is remarkable because it suggests the VO nonlocal approach as a theoretically consistent and computationally efficient basis to complement the discovery and algorithmic design of a wide class of heterogeneous solids [41] such as, for example, metamaterials [12,42,43], lattice structures [44][45][46], and functionally-graded solids [6,30], and porous solids [10,11]; where heterogeneous nonlocality is a very natural outcome of the material heterogeneity [6,30] and geometric configurations [7,47,48].…”