Contributions: produced part of the samples, performed part of the experiments and analyzed the data, performed part of the computational analysis and participated in the writing of the manuscript. Contributions: performed mechanical experiments and analyzed the data, performed the computational analysis and participated in writing the manuscript. Contributions: fabricated microscale samples, performed nanomechanical tests and analyzed the data, performed the mechanical numerical analysis and participated in writing the manuscript.
Contributions: performed experiments and analyzed the data, performed part of the numerical analysis, wrote the manuscript.
LIST OF TABLES
NOMENCLATURE
INTRODUCTION TO ARCHITECTED MATERIALS
After stabilization of the formed bubbles, the mixture can be polymerized to become solid [46]. By performing the same type of dimensional analysis, expressions for the collapse of the cells (i.e. the strength) were obtained in the form [46]. Static determination requires that the forces in each member be known from the equilibrium equations, while kinematic determination implies that the unique position of each joint can be determined based on the lengths of the supports.
Moreover, the first part of the thesis deals with the response of these materials under quasi-static loading, while the second part investigates their response in the dynamic regime.
IDENTIFYING THE EFFECT OF NODES ON LATTICE ARCHITECTURES
This is done to mitigate the effect of the toe area on the stiffness measurement. Figures (i) are CAD models of the entire structures, (ii) are SEM images of the entire structures, (iii) are CAD models of unit cells, (iv) are representative nodes showing the average nodal connectivity, and (v) are SEM images from the top of the structures . The stiffness of the rigid beam model is similar to the rigid model but has an additional term in the numerator.
This is what set the relative density limit for the solid polymer samples in this work.
IMPACT OF NODE GEOMETRY ON NON-SLENDER LATTICE ARCHITECTURES
To take into account the effect of the nodes, that is, the beam connections, we use rotational springs with variable stiffness at crossings in addition to beam elements. A significantly more pronounced effect of the nodal stiffness nkθ is observed in the non-rigid structure than in the rigid one. This setup allowed us to arbitrarily change the nodal geometry independently of the strut cross-section.
The DOFs of the beam elements at the gage section ends were coupled to the six DOFs maintained at each end circular cross section. The node substructures used in the validation consisted of half of the internal node substructures shown in Figs. The stress-strain data also conveys the effective strength of the samples, which is beyond the scope of this study (specially designed joint geometries create complex stress concentrations that could not be systematically studied within the given configuration).
The non-rigid tetrakaidecahedron, on the other hand, has most of the strain energy localized at the nodes throughout the (r/l) range indicating bending-dominated deformation and higher sensitivity to node geometry throughout. To capture the divergence of the simulations from classical stiffness predictions at higher (r/l) ratios, we include a higher-order term in the classical scaling law. This indicates that this term accounts for the bending of the beams enabled by the nodes at high (r/l) ratios [94].
For the non-rigid architectures, we study the simplest 2D representation of a diamond structure shown in Fig.3.1b (except without rotational springs) to understand the nature of the higher-order exponent. Experiments and simulations have shown a more pronounced effect of the nodes on the stiffness of non-rigid grid architectures than that of rigid ones.
NODELESS ARCHITECTURES VIA SELF-ASSEMBLED GEOMETRIES
The circular marker indicates the stress and strain of the partially compressed nanolattice shown in (c). We first simulated uniaxial compression of each architecture along each ei direction for ie. directions and [001] directions, respectively, similar to actual experimental boundary conditions, to allow comparison with experimental anisotropy values in these three directions. The contoured elastic surfaces were then plotted using all values of Enormalized by Young's modulus of ALD alumina, Es, where colors represent the magnitude of the normalized modulus (Fig. 4.3b, inset).
Top row: micrographs before and after 3 cycles of in situ uniaxial compressions toε = 30%. the maximum load in the nano-indenter was reached before the 168 nm sample failed). We attribute the observed mechanical resilience to the double curvature of the alumina surfaces. We quantify the architectural morphology by extracting the point-wise mean and Gaussian curvatures and calculating the main curvature probability distribution (that is, the distribution of κ1. and κ2).
The surface-to-volume ratio of these unit cells was matched to that of the double-bonded columnar architecture (Figure 4.9) to ensure equivalent relative densities. Performing the same analysis for the other nano-labyrinth architectures was consistent with scaling of the columnar stiffness with scaling exponents ranging from 1.16 to 1.21 in the h100i directions, which remained below the calculated scaling exponents. To further understand the effect of double curvature on the load distribution within the shells, we analyzed first-order approximations of the columnar architecture, as the exact morphology of nano-labyrinth architectures is difficult to quantify.
To predict the full elastic response of the architectures (i.e., elastic surfaces and Young's moduli in all directions), we implemented a numerical homogenization scheme. For the recoverable samples (ie, some of the . 44 nm samples and all of the 11 nm samples), the strength was calculated using the 0.2% strain compensation method.
VIBRATION MITIGATION VIA LATTICE ARCHITECTURES
A square grid with 5µm spacing was also formed on the substrate to prevent delamination of the Si thin film under the microgrid (Fig.5.1c). The buckling pattern vertically transcended all out-of-plane layers through the rotation of the vertical posts (Fig.5.1f). For as-fabricated Si microlattices, we used the same geometry of the experimental samples described above.
For this purpose, we calculated the dispersion ratio of the lithiated microgrid immersed in the electrolyte, while taking into account the coupling between the liquid and the solid. Using advanced fabrication techniques, we embed µm-scale resonators in the unit cells of the material and experimentally demonstrate the existence of numerically predicted band gaps. To design architected materials with band gaps, we used a variation of the auxetic unit cell design proposed by Krödel et al.
The dispersion relation for the unmodified unit cell (Fig. 5.12) shows no band gaps, while that of the unit cell containing the resonator showed the appearance of a band gap centered at ~1.4 MHz. Pure cantilever beam resonance is observed in the kHz regime. in a spring-mass system), whose resonant frequency can be approximated as f0 = 1. To experimentally measure the band gap in the dispersion relation, we fabricated 10 × 48 × 16 wires (in the x-directions, y-, and z- , respectively) of the unit cells in Fig.
To promote proper contact with the transducers, a 6µm plate was printed on the plus and minusx faces of the microgrids. To confirm the existence of the band gap, we investigated the material using a chirp with a frequency content of 1 MHz to 3 MHz.
DYNAMIC LOADING ON CARBON-BASED LATTICE ARCHITECTURES
Bending of the carbon phase without a matrix showed catastrophic failure, as observed in the compression tests. The impact reaction of the SiO2 spheres on Si was characterized by distinct re-bound and shattering regimes. The last images in this sequence show catastrophic failure of the particle, which disintegrated into several pieces like the one shown in Fig. 6.15d.
Normalizing the rebound and inelastic energies by the impact energy and plotting those values as a function of the impact energy in Fig. The impact of the SiO2 particles on tetrakaide cahedron architectures showed three different response regimes: (i) elastic impact, (ii) cratering and particle rebound, and (iii) cratering and particle trapping, depending on the relative density of the carbon material and the impact energy. The slope of 0.69 corresponding to the inelastic energies indicates that this material can dissipate on average 69% of the impact energy in the regime under investigation.
Close-up of the crater base on the ρ ≈ 17% sample impacted at a velocity of 255 m/s shows characteristic indications of brittle failure in the carbon supports. Full penetration of the ρ=8% sample was observed before the impact at 749 m/s, and deep particle embedding was observed in the ρ=17% sample at 757 m/s. To capture the deflection of the truss-core sandwich plate, two high-speed cameras (HPV-X2, Shimadzu) were mounted above the blast setup to allow in situ digital image correlation (DIC).
The carbon and carbon-epoxy cores fractured but prevented plastic deformation of the faceplates. Most of the explorations in the field of nano-architectural materials have been guided by the search for hard, strong and deformation-resistant materials.
BIBLIOGRAPHY
Large strain response of additively manufactured FCC metamaterials: From octet beam lattices to continuous shell mesostructures. Effects of Ag on elastic modulus values of nanoporous Au foams.Journal of Materials Research. New functional insights into the internal architecture of laminated anchors of Euplectella aspergillum. Proceedings of the National Academy of Sciences.
Effective property evaluation and analysis of three-dimensional periodic lattices and composites through Bloch wavelet homogenization. Journal of the Acoustic Society of America. Influence of joint geometry on the effective stiffness of three-dimensional non-thin lattice architectures. Deformation behavior and energy absorption capacity of polymer and ceramic-polymer composite microlattices under cyclic loading.Journal of Materials Research.
International Journal of Solids and Structures Flexural behavior of elliptical cylindrical shells and tubes under compression. Response of sandwich structures with pyramidal beam cores under compression and impact loading. Composite structures.
SUPPLEMENTARY VIDEOS
Impact of SiO2 particles on ρ≈ 17% tetrakaidecahedron carbon nanogrid at v0 = 238m/s and rebounding at vr =50m/s, exhibiting cratering and ejection.
