Computational characterization of the wave propagation behavior of multi-stable periodic cellular materials

Abstract

In this work, we present a computational analysis of the planar wave propagation behavior of a one-dimensional periodic multi-stable cellular material. Wave propagation in these materials is interesting because they combine the ability of periodic cellular materials to exhibit stop and pass bands with the ability to dissipate energy through cell-level elastic instabilities. Here, we use Bloch periodic boundary conditions to compute the dispersion curves and introduce a new approach for computing wide band directionality plots. Also, we deconstruct the wave propagation behavior of this material to identify the contributions from its various structural elements by progressively building the unit cell, structural element by element, from a simple, homogeneous, isotropic primitive. Direct integration time domain analyses of a representative volume element at a few salient frequencies in the stop and pass bands are used to confirm the existence of partial band gaps in the response of the cellular material. Insights gained from the above analyses are then used to explore modifications of the unit cell that allow the user to tune the band gaps in the response of the material. We show that this material behaves like a locally resonant material that exhibits low frequency band gaps for small amplitude planar waves. Moreover, modulating the geometry or material of the central bar in the unit cell provides a path to adjust the position of the band gaps in the material response. Also, our results show that the material exhibits highly anisotropic wave propagation behavior that stems from the anisotropy in its mechanical structure. Notably, we found that unlike other multi-stable cellular materials reported in the literature, in the system studied in this work, the configurational changes in the unit cell corresponding to its different stable phases do not significantly alter the wave propagation behavior of the material.

Analysis of the directionality on periodic materials

“…A porosity of 0.0 represents a homogeneous material, used as a reference in this case. As expected, the directionality of the material increases with porosity, and the higher values for the averaged group speed happens along the x and y axes where we have continuous paths for the wave to propagate (Valencia et al, 2019b). Notice that the resulting curves are symmetric with respect to rotations of 90 For comparison, we present the isofrequency contours for the first three branches of the dispersion relations for this material in Figure 13 (Guarín-Zapata et al, 2020).…”

“…This interest is related to the appearance of unusual properties such as effective negative mass, negative refraction, negative Poisson equation, and acoustic/electromagnetic cloaking (Norris and Haberman, 2012;Hussein et al, 2014;Goldsberry and Haberman, 2018). Thus, there is a trend in designing microstructures aiming to control the bulk properties (Milton and Cherkaev, 1995;Norris and Nagy, 2011;Willis, 2016;Valencia et al, 2019b;Guarín-Zapata et al, 2019). Although direct numerical simulations, where the bulk of the material is considered and the complete microstructure is discretized are possible (Sigalas and Garcıa, 2000), the most common approach is to take advantage of the periodicity of the material and model a single cell (Pennec et al, 2010;Hussein et al, 2014).…”

On‐Board Mechanical Control Systems for Untethered Microrobots

“…[74,75] These mechanisms, in turn, can communicate information by guiding acoustic or electromagnetic waves. [74,[76][77][78][79][80] It has been envisioned that conformable monolithic systems that undergo complex motion directly programmed within the architecture of the material will realize soft robots capable of transforming a simple input, such as a pressure impulse, into a complex sequence of flexion, tension, and torsion outputs. [81] The programmed response can be initiated by the environment with the use of stimuli-responsive materials.…”

Research on hierarchical cylindrical negative stiffness structures’ energy absorption characteristics

“…NS structures are a class of mechanical metamaterials that have gained significant attention due to their reusability [1][2][3][4] and potential applications in various fields, such as vibration control [5][6][7][8][9][10][11][12][13], energy absorption [4,[14][15][16][17][18][19][20][21], and actuation [22][23][24][25][26][27][28][29][30][31]. It is of particular importance in the area of energy absorption, as it can absorb energy through its multistable property [32][33][34][35][36][37][38][39] and dissipate it with a snap-back behavior [7,35,[40][41][42][43][44], rather than through plastic deformation…”