Individual Unit Cells Research Articles

A Multi-Sized Unit Cell Method for the Design of LPBF Lattice Support Structures Concerning Complex Geometries

Abstract Composed of individual unit cells strategically arranged to achieve a desired function, lattices are a promising solution for laser powder bed fusion (LPBF) support structure design in additive manufacturing. Despite their many advantages (e.g., multifunctionality and reduced material cost), prior work in lattice support structure design primarily focuses on horizontal support domains that are not translatable to support domains for complex geometries, thereby limiting their application. This work introduces a multi-sized unit cell design optimization (MSO) method to create lattice support structures (LSS) for parts with complex geometries. The proposed method utilizes voxelization to generate LSS using box-like unit cells of different sizes. It also allows for efficient, high-dimensional design optimization for the types and locations of user-specified unit cells through a modified simulated annealing-based optimization algorithm. The effectiveness and efficiency of the MSO method are demonstrated through the case study of an adapter pipe for a high-temperature heat exchanger. For this demonstration, LSS using multi-sized unit cells are designed to increase heat transfer rate while satisfying structural integrity and material cost constraints. The case study results indicate that the design of the LSS derived from the MSO method fulfills all constraints, including the design constraint of 50% material cost reduction, compared to the solid support structure. In contrast, the lattice support structure designs derived from equal-sized unit cell methods either cannot satisfy all design constraints or have a lower heat transfer rate than the design of the MSO method.

Homogenization of quasi-periodic conformal architectured materials and applications to chiral lattices

In this study, we propose to extend asymptotic periodic homogenization for non-periodic continuous microstructured media, assuming that the non-periodic geometry (called quasi-periodic) can be designed by a conformal planar transformation of a periodic parent domain architectured media with periodically disposed unit cells. Conformal transformations are shown to play a privileged role in the design of circular macroscopic heterogeneous domains tessellated with non-periodic unit cells, obtained from a periodic parent domain architectured with these unit cells. The conditions for conformal invariance are established, leading to the general form of conformal transformation in their dependencies upon the periodic coordinates. It is shown that any conformal map can be decomposed into the product of an isotropic dilatation function of the first periodic spatial position of decreasing exponential type and a rotation characterized by an angular function linear in the second periodic position. A general theory of quasi-periodic homogenization in the framework of conformal transformations is established for the first time, leading to an expression of the tensor of quasi-periodic moduli which is fully evaluated from the solution of the elasticity boundary value problem posed over the periodic unit cell. The influence of microcurvature distortion of individual unit cells on their effective properties is evaluated. Closed-form solutions are confronted to numerical examples issued from the implementation of circular periodicity in a finite element solver, showing overall a good agreement with the identified homogenized moduli.

High-resolution three-dimensional imaging of topological textures in nanoscale single-diamond networks.

Topological defects-extended lattice deformations that are robust against local defects and annealing-have been exploited to engineer novel properties in both hard and soft materials. Yet, their formation kinetics and nanoscale three-dimensional structure are poorly understood, impeding their benefits for nanofabrication. We describe the fabrication of a pair of topological defects in the volume of a single-diamond network (space group Fd m) templated into gold from a triblock terpolymer crystal. Using X-ray nanotomography, we resolve the three-dimensional structure of nearly 70,000 individual single-diamond unit cells with a spatial resolution of 11.2 nm, allowing analysis of the long-range order of the network. The defects observed morphologically resemble the comet and trefoil patterns of equal and opposite half-integer topological charges observed in liquid crystals. Yet our analysis of strain in the network suggests typical hard matter behaviour. Our analysis approach does not require a priori knowledge of the expected positions of the nodes in three-dimensional nanostructured systems, allowing the identification of distorted morphologies and defects in large samples.

Hierarchical Composites Patterned via 3D Printed Cellular Fluidics

AbstractAdditive manufacturing of freeform structures containing multiple materials with deterministic spatial arrangement and interactions remains a challenge for most 3D printing processes, due to complex fabrication tool requirements and limitations in printability of some material classes. Here, a versatile method is reported to produce architected composites using the concept of cellular fluidics, in which lattices of unit cells are used as templating scaffolds to guide flowable infill materials in a programmed spatial pattern, upon which they are cured in place to produce a deterministically ordered multimaterial solid. The lattice design relies on the unit cell size, type, strut diameter, surface wetting, and distribution of cellular structures to control liquid flow and retention. Individual unit cells are tuned to achieve reliable infilling and combined into higher‐order architectures to achieve multiscale composite materials with disparate mechanical properties, including those considered non‐printable. Lattice design considerations for leveraging capillary phenomena and demonstrate several methods of patterning polymers in 3D‐printed cellular fluidic structures are presented. The concept of tuning the compressive response of an architected composite using a flexible‐elastomer as the lattice and a stiff‐epoxy as the infill material is illustrated.

Reconfigurable Metamaterial Antenna based an Electromagnetic Ground Plane Defects for Modern Wireless Communication Devices

In this paper, a design of a microstrip antenna based on metamaterial (MTM) and electromagnetic band gap (EBG) arrays. The patch is structured from 5×3 MTM array to enhance the antenna bandwidth gain product. The individual unit cell is structured as a split ring (SRR) with a T-resonator. The ground plane is defected with an EBG to suppress the surface waves diffraction from the substrate edges. The antenna is printed on a Roger substrate with permittivity of 10.2 and 1 mm thickness. It is found that the proposed antenna provides a frequency resonance around 2.45 GHz and 3.5 GHz with another band between 4.6 GHz to 5.6 GHz which are very suitable for Wi-Fi and 5G networks. Nevertheless, the antenna gain is found to vary from 3.5 dBi to less than 6 dBi. The antenna size is reduced enough to λ/5 of the guided wavelength to fit an area of 12 mm×20 mm. The proposed antenna performance is controlled with two PIN diodes for reconfiguration process. The antenna frequency resonance bands are found to be well controlled by stopping the current motion at the particular band. The antenna is fabricated and tested experimentally. Finally, the simulated results are compared to those obtained from measurements to provide an excellent agreement to each other with error of less than 3%.

Design Optimization of Lattice Structures Under Impact Loading for Additive Manufacturing

Abstract Additive manufacturing (AM) has enabled the production of intricate lattice structures with excellent performance and minimal mass. Design approaches that consider static loading, including lattice-based topology optimization (TO), have been well-researched recently. However, to date, there appears to be no widely accepted method of optimizing lattice structures for high-strain rate loading, especially when the design for additive manufacturing (DFAM) principles are considered. This study proposes a computational framework for the design of lattice structures under specified impact loading. To manage dimensionality while achieving sufficient generality, a heuristic design space is developed that relies on traditional TO to govern the design's macrostructure and standard dimensioning to govern its mesostructure. DFAM principles are then incorporated into a Bayesian optimization scheme wrapped around traditional TO to achieve manufacturable designs that absorb high-impact loading. Because this approach does not require analytical gradient information, the framework can be used to optimize directly on complex objectives, such as injury metrics calculated from the acceleration curve. A series of case studies is formulated around a mass-performance tradeoff and involves individual unit cell design as well as full-part design. The proposed design parameterization is found to enable sufficient flexibility to achieve consistently good performance regardless of AM build orientation.

Multiscale electric-field imaging of polarization vortex structures in PbTiO3/SrTiO3 superlattices

In ferroelectric heterostructures, the interaction between intrinsic polarization and the electric field generates a rich set of localized electrical properties. The local electric field is determined by several connected factors, including the charge distribution of individual unit cells, the interfacial electromechanical boundary conditions, and chemical composition of the interfaces. However, especially in ferroelectric perovskites, a complete description of the local electric field across micro-, nano-, and atomic-length scales is missing. Here, by applying four-dimensional scanning transmission electron microscopy (4D STEM) with multiple probe sizes matching the size of structural features, we directly image the electric field of polarization vortices in (PbTiO3)16/(SrTiO3)16 superlattices and reveal different electric field configurations corresponding to the atomic scale electronic ordering and the nanoscale boundary conditions. The separability of two different fields probed by 4D STEM offers the possibility to reveal how each contributes to the electronic properties of the film.

Letter to the Editor: Structural transitions of the vitreous state

The presence of structural nanoheterogeneity means that sharp structural transitions at a well defined temperature or composition are an anathema to the vitreous state. Hence they should not be expected, but rather an extended transition, whose width is defined by the form and length scale of the relevant nanoheterogeneity. It should also be noted that all of the vitreous state transitions considered here, together with crystallisation at the melting point, are spatially non-uniform. This behaviour should be compared to sharp transitions that occur within the crystalline state, for example the displacive transition between α- and β-quartz, and those from a paramagnetic to a magnetically-ordered state. Such sharp transitions involve simultaneous co-operative movements across a large number identical unit cells, and hence cannot occur in the absence of a periodic structure. As a result, they are sensitive to disorder within individual unit cells, as may be seen from the case of cristobalite, where the presence of disorder reduces the αβ transition temperature, and in extremis inhibits the transition from β- to α-cristobalite.

Computationally Efficient Surrogate-Assisted Design of Pyramidal-Shaped 3-D Reflectarray Antennas

Reflectarrays (RAs) have been attracting considerable interest in recent years due to their appealing features, in particular, the possibility of realizing pencil-beam radiation patterns, as in the phased arrays, but without the necessity of incorporating the feeding networks. These characteristics make them attractive solutions, among others, for satellite communications or mobile radar antennas. Notwithstanding, available microstrip implementations are inherently narrow-band and heavily affected by conductor and surface wave losses. RAs based on grounded dielectric layers offer improved performance and flexibility in terms of shaping the phase reflection response. In either case, a large number of variables (induced by the need for independent adjustment of individual unit cell geometries) and the necessity of handling several requirements make the design process of reflectarrays a challenging endeavor. In particular, RA optimization is extremely expensive when conducted at the level of electromagnetic (EM) simulation models, otherwise necessary to ensure reliability. A practical solution is a surrogate-assisted design with the metamodels constructed for the RA unit elements. Unfortunately, conventional modeling methods require large numbers of training data samples to render accurate surrogates, which turns detrimental to the optimization process efficiency. This work proposes an alternative approach with the unit element representations constructed using deep learning with automated adjustment of the model architecture. As a result, design-ready surrogates can be constructed using only a few hundred samples, and the total RA optimization cost is reduced to only a handful of equivalent EM analyses of the entire array. Our approach is validated using an RA incorporating 3-D pyramidal-shaped elements and favorably compared to benchmark techniques. Experimental verification of the obtained design is discussed as well.

Photoinduced Ultrafast Transition of the Local Correlated Structure in Chalcogenide Phase-Change Materials.

Revealing the bonding and time-evolving atomic dynamics in functional materials with complex lattice structures can update the fundamental knowledge on rich physics therein, and also help to manipulate the material properties as desired. As the most prototypical chalcogenide phase change material, Ge_{2}Sb_{2}Te_{5} has been widely used in optical data storage and nonvolatile electric memory due to the fast switching speed and the low energy consumption. However, the basic understanding of the structural dynamics on the atomic scale is still not clear. Using femtosecond electron diffraction, structure factor calculation, and time-dependent density-functional theory molecular dynamic simulation, we reveal the photoinduced ultrafast transition of the local correlated structure in the averaged rocksalt phase of Ge_{2}Sb_{2}Te_{5}. The randomly oriented Peierls distortion among unit cells in the averaged rocksalt phase of Ge_{2}Sb_{2}Te_{5} is termed as local correlated structures. The ultrafast suppression of the local Peierls distortions in the individual unit cell gives rise to a local structure change from the rhombohedral to the cubic geometry within ∼0.3 ps. In addition, the impact of the carrier relaxation and the large number of vacancies to the ultrafast structural response is quantified and discussed. Our Letter provides new microscopic insights into contributions of the local correlated structure to the transient structural and optical responses in phase change materials. Moreover, we stress the significance of femtosecond electron diffraction in revealing the local correlated structure in the subunit cell and the link between the local correlated structure and physical properties in functional materials with complex microstructures.

Investigating the stochastic dispersion of 2D engineered frame structures under symmetry of variability

Additive manufacturing has enabled the construction of increasingly complex mechanical structures. However, the variability of mechanical properties may be higher than that of conventionally manufactured structures. Typically, the computational cost of the numerical modeling of such structures considerably increases when variability is considered. In deterministic analyses of periodic structures, the dispersion diagrams obtained for the first Brillouin zone (FBZ) can be used to predict attenuation bands for any direction of propagation. This can be further simplified considering only the contour of the irreducible Brillouin zone (IBZ) if the unit cell presents symmetries. The objective of the current investigation is to present evidence that, similarly to what occurs in deterministic cases, the stochastic results obtained by scanning only the IBZ contour of the proposed two-dimensional unit cell under 4-fold rotational symmetry of statistical variability coincides with statistical results obtained scanning the FBZ. This is not a direct result, because each individual unit cell sample is asymmetric. We show that, under symmetry of variability statistics, the stochastic results computed for supercells and for finite metastructures consisting of a finite number of cells also coincide with the results for the IBZ contour of the unit cell. This result is important, as it dramatically reduces the computation cost of the stochastic analysis of such structures.

Systematic design of Cauchy symmetric structures through Bayesian optimization

Using a new Bayesian Optimization algorithm to guide the design of mechanical metamaterials, we design nonhomogeneous 3D structures possessing the Cauchy symmetry, which dictates the relationship between continuum and atomic deformations. Recent efforts to merge optimization techniques with the design of mechanical metamaterials has resulted in a concentrated effort to tailor their elastic and post elastic properties. Even though these properties of either individual unit cells or homogenized continua can be simulated using multi-physics solvers and well established optimization schemes, they are often computationally expensive and require many design iterations, rendering the validation stage a significant obstacle in the design of new metamaterial designs. This study aims to provide a framework on how to utilize miniscule computational cost to control the elastic properties of metamaterials such that specific symmetries can be accomplished. Using the Cauchy symmetry as a design objective, we engineer structures through the strategic arrangement of 5 different unit cells in a 5×5×5 cubic symmetric microlattice structure. This lattice design, despite constituting a design space with 510 3D lattice configurations, can converge to an effective solution in only 69 function calls as a result of the efficiency of the new Bayesian optimization scheme. To validate the mechanical behavior of the design, the lattice structures were fabricated using multiphoton lithography and mechanically tested, revealing a close correlation between experiments and simulated results in the elastic regime. Ultimately, a similar methodology can be utilized to design metamaterials with other material properties, aspiring to control properties at different length scales, an endeavor that requires inordinate computation cost.

Analytical and numerical modeling of reconfigurable reflecting metasurfaces with capacitive memory

In this article, we develop analytical–numerical models for reconfigurable reflecting metasurfaces (MSs) formed by chessboard-patterned arrays of metallic patches. These patch arrays are loaded with varactor diodes in order to enable surface impedance and reflection phase control. Two types of analytical models are considered. The first model based on the effective medium approach is used to predict the MS reflectivity. The second model is the Bloch wave dispersion model for the same structure understood as a two-dimensional transmission line metamaterial. The latter model is used to study ways to suppress parasitic resonances in finite-size beamforming MSs. We validate the developed analytical models with full-wave numerical simulations. Finally, we propose a design of the MS control network with capacitive memory that allows for independent programming of individual unit cells of the beamforming MS.

New explanation for the existence of B19′ phase in NiTi alloy from the perspective of twinning martensite

The ground state structure of NiTi martensite in experiments and existing theoretical calculations is the focus of ongoing disagreements. Based on Waitz et al.’s (2004, 2007) experiments, we use the first principle calculations to investigate the effect of (001) twin interface and thickness on the stability of NiTi martensite. Moreover, we determine the interface of the (001) martensitic twins observed in the experiment as the interface of twinned supercell-1 (TSC-1), in which the lattice parameters of individual unit cells are close to the experimental measurements of B19′. Furthermore, the energy per atom for TSC-1 is always between that of B19′ and B33 and does not vary with the twin thickness. Considering the structural similarity of TSC-1 and B33, an energy barrier between TSC-1 and B33 via the minimum enthalpy pathways was demonstrated. The influence of the (001) twin interface could proves the rationality of the existence of B19′ in experiments.

FDTD Simulations of Modulated Metasurfaces with Arbitrarily Shaped Meta-atoms by Surface Impedance Boundary Condition

In this paper, we propose a reduced-complexity finite difference time domain (FDTD) simulations of modulated metasurfaces with arbitrary unit cells. The three dimensional (3D) physical structure of the metasurface is substituted by a spatially varying surface impedance boundary condition (IBC) in the simulation; as the mesh size is not dictated by sub-wavelength details, considerable advantage in space- and time-step is achieved. The local parameters of the IBC are obtained by numerical simulation of the individual unit cells of the physical structure, in a periodic environment approximation, in the frequency domain. As the FDTD requires an appropriate time domain impulse-response, the latter is obtained by broad-band frequency simulations, and vector fitting to an analytic realizable time response. The approach is tested on metasurface structures with complex unit cells and extending over 10 ××10 wavelengths, using a standard PC with 64GB RAM.

Thermomechanical behavior of polymeric periodic structures

Additive manufacturing (AM) enables the fabrication of periodic structures with regular repeat units and tailorable mechanical properties. Polymer-based AM processes, such as fused filament fabrication (FFF), permit rapid, low-cost fabrication of periodic structures from a wide range of materials. However, the mechanical properties of polymers are strongly affected by temperature, especially near the glass transition temperature (T g ), which has a significant impact on the design and application of the structures. Herein, we utilize a coupled experimental and computational approach to evaluate the mechanical behavior of polymeric periodic structures (PPS) with uniform and spatially varying temperatures that span T g . Individual unit cells (square, auxetic, and honeycomb) are additively manufactured from polylactic acid (PLA) (T g = 54 °C) and experimentally evaluated by dynamic mechanical analysis (DMA) using a tension test fixture and thermal chamber. The unit cells are subjected to sequential tension and compression tests, up to a maximum of +/−20% strain, which are repeated from 40 °C to 65 °C in 5 °C increments. Maximum forces vary by two orders of magnitude when temperature varies across T g , and a hysteresis loop is observed for temperatures 14 °C below T g . This indicates that viscoelasticity has a significant impact on the mechanical properties of the structure below T g and that the structures are capable of dissipating energy. Experimental force-displacement and energy dissipation results agree favorably with results from a multiphysics finite element framework, which utilizes bulk material properties as inputs. The computational framework is then applied to structures comprising tessellated unit cells to evaluate the effects of uniform temperatures and temperature gradients on mechanical properties. The results demonstrate that non-uniform temperature fields can produce spatial variation of mechanical properties, such as Poisson’s ratio, throughout the structure. Insight obtained in this investigation provides guidelines for the design, fabrication, and implementation of PPS operating across a range of temperatures that passively modifies their mechanical properties and energy dissipation characteristics. • Thermomechanical analysis of square, honeycomb, and auxetic periodic structures. • Experimental and computational analysis of 3D printed PLA across glass transition. • Thermal gradients spatially affect array mechanical properties (Poisson’s ratio). • Square unit cell and honeycomb array dissipate highest energy per unit mass. • Applicable to other polymers and structures by updating bulk finite element inputs.

Structural topology optimization of 3D‐printable microlattices for lightweight materials

AbstractWe present a micro‐macro approach for the structural optimization of graded microlattices that contain unit cells with a triply periodic structure. These individual unit cells are based on minimal surface problems such as the the Schwarz Primitive surface or the Gyroid and exhibit a porous structure that allows for a macroscopic grading of the material fraction of the cells. Both the macro‐scale and the micro‐scale are optimized by means of a Cahn‐Hilliard phase‐field model that is coupled with an elastic problem. The optimization on the macro‐scale is performed with the finite element method (FEM) while the micro‐scale optimization makes use of a spectral method that solves the periodic problem in a fast manner by means of fast Fourier transforms (FFT).

A Modified Compact Tension Test for Characterization of the Intralaminar Fracture Toughness of Tri-Axial Braided Composites.

The application of braided composite materials in the automotive industry requires an in-depth understanding of the mechanical properties. To date, the intralaminar fracture toughness of braided composite materials, typically used for describing post-failure behavior, has not been well-characterized experimentally. In this paper, a modified compact tension test, utilizing a relatively large specimen and a metallic loading frame, is used to measure the transverse intralaminar fracture toughness of a tri-axial braided composite. During testing, a relatively long fracture process zone ahead of the crack tip was observed. Crack propagation could be correlated to the failure of individual unit cells, which required failure of bias-yarns. The transverse interlaminar fracture toughness was found to be two orders of magnitude higher than the reference interlaminar fracture toughness of the same material. This is due to the fact, that intralaminar crack propagation requires breaking of fibers, which is not the case for interlaminar testing.

Design of a one-dimensional underwater acoustic leaky wave antenna using an elastic metamaterial waveguide

Acoustic imaging in water traditionally relies on phased arrays of active electro-acoustic transducers to steer acoustic energy in specific directions. One potential alternative approach to steer acoustic beams is to use a single transducer attached to a dispersive antenna that radiates or receives acoustic energy from different directions as the frequency of operation changes. This is known as a leaky wave antenna (LWA). While LWAs have been proven effective in beam steering for electromagnetic and air-borne acoustic waves, the design of an analog device in water presents a unique challenge due to the low contrast in acoustic impedance between elastic solids and water, which necessitates the consideration of fluid-elastic coupling in the design of the elastic LWA. This work presents an approach to design an elastic metamaterial waveguide coupled to an external fluid domain as one means to create an acoustic LWA for underwater operation. Forward-to-backward radiation is achieved through the design of mass-in-cavity structures that produce simultaneous negative effective mass and modulus by considering fluid-elastic coupling. The design is presented through finite element analysis of individual unit cells and a water-loaded elastic LWA. A design example is presented that steers through backfire to endfire as a function of input frequency.

Reconfigurable THz Metamaterial Filter Based on Binary Response for Information Processing System

Light-matter interactions between the metallic and dielectric layers along with the controlling of electromagnetic waves can create a way to develop micro-devices and moderate the functionalities for advanced applications. This study describes a new controlling technique of the plasmatic electron packet based on an electric split-ring resonator (eSRR). All numerical experiments were performed using an advanced CST electromagnetic package. The proposed metamaterial tunneled structure in this study operates using terahertz (THz) frequency spectrum as an efficient digital processing filter. The array combination of the tunneled structure consisted of three individual unit cells. Moreover, the two engineered metallic arms added to the tunneled structure exhibited two peak resonances and one passband frequency region. A large evanescent field was produced to enhance the wave-metal interactions with the presence of a metal-dielectric micro-tunnel. The intensity of the electromagnetic wave-metal interactions was encoded to binary 0 and 1 for information encoding purposes. As a result, the reconfigurable micro-unit cell metamaterial tunneled structure was able to effectively control the electric field and allow electron packets to be digitally encoded for the information processing system.