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Micro-architected material design for mechanical response

Rapid advances in additive manufacturing (AM) have enabled the creation of micro-architected materials—also known as mechanical metamaterials—with unprecedented control over fine-scale geometries and arrangements of multiple material constituents. These “materials” can achieve unique and extraordinary effective mechanical properties through their complex architectures rather than composition alone. A key challenge is to design for these bespoke effective mechanical responses within the constraints of available AM techniques (i.e., given a set of desired effective properties), identify a (often nonunique) micro-architecture and selection of material constituents that achieves them. Two main strategies have emerged. Gradient-based methods use sensitivity analysis to iteratively refine candidate designs, while data-driven methods learn micro-architecture-constituent relationships from existing examples to propose new designs. This article reviews these design approaches for micro-architected materials with tailored mechanical responses that can be fabricated by AM as well as their applications.

Spadaccini, Christopher M [Lawrence Livermore Nati↗

Investigating Porous Media for Relief Printing Using Micro-Architected Materials

Advances in printed electronics are predicated on the integration of sophisticated printing technologies with functional materials. Although scalable manufacturing methods, such as letterpress and flexographic printing, have significant history in graphic arts printing, functional applications require sophisticated control and understanding of nanoscale transfer of fluid inks. In this paper, a versatile platform is introduced to study and engineer printing forms, exploiting a microscale additive manufacturing process to design micro-architected materials with controllable porosity and deformation. Building on this technology, controlled ink transfer for submicron functional films is demonstrated. The design freedom and high-resolution 3D control afforded by this method provide a rich framework for studying mechanics of fluid transfer for advanced manufacturing processes.

36 MATERIALS SCIENCE↗

Anisotropic yield models for lattice unit cell structures exploiting orthotropic symmetry

We report numerical homogenization enables efficient computational analysis and design of multiscale structures made of micro-architected materials including lattice unit cells. However, predicting yield is nontrivial because it requires accurate and efficient predictions of the maximum stress inside the homogenized unit cells. To address this challenge, we develop a macroscale anisotropic yield function for micro-architected materials. The yield function depends on the three-dimensional macroscale stress state and the parameters describing a family of micro-architectures, such as the radii of the struts in a lattice unit cell. To ensure accuracy, we determine the maximum stress using three-dimensional continuum finite-element analysis. To ensure efficiency, we construct surrogate models from the aforementioned high-fidelity results for yield prediction. To reduce simulation costs and surrogate modeling complexity, we leverage orthotropic symmetry commonly found in lattice unit cells. In this paper, we provide a thorough presentation of group representations and the systematic procedure to exploit orthotropic domain symmetry in homogenization and surrogate modeling. We illustrate the use of linear homogenization results to predict yield in specific unit cells without further simulations. We furthermore show that surrogate modeling presents a viable option for anisotropic yield prediction in a continuously parametrized family of micro-architectures. More specifically, despite the dimensionality and degree of nonlinearity in the maximum micro von Mises stress within the unit cell, the surrogate models can predict it with less than 5% error at least 90% of the time. Moreover, the largest under-prediction error, which is more critical than the over-prediction error, is typically less than 10%.

42 ENGINEERING↗

Embedded 3D printing of isotropically enhanced lattice structure with programmable elasticity via three-dimensional fiber alignment

Engineered composites with fiber orientation in a complete three-dimensional (3D) context are highly desired for maximizing structural performance as they mimic the well-organized fiber arrangement in natural composites. However, most fabrication techniques lack the capability for through-plane (z-axis) alignment, limiting the possibility for structural design and performance optimization. In this study, we present an embedded 3D printing approach that enables complete 3D fiber alignment, including region-specific alignment control along the through-plane direction. Our method utilizes the extrusion and suspension of composite inks within a supporting matrix. By regionally adjusting the ink extrusion rate and nozzle translation rate, we locally manipulated the fiber arrangement within the composite 3D architecture. Here, we demonstrate that the 3D alignment of carbon fibers in a structural composite significantly enhances both mechanical properties and thermal conductivity in the in-plane and through-plane directions. Furthermore, by strategically arranging regional fiber orientations within micro-architected materials, we fabricated metamaterial engineered composites with programmable anisotropy ratio and directional moduli.

36 MATERIALS SCIENCE↗

Tailored ultrasound propagation in microscale metamaterials via inertia design

The quasi-static properties of micro-architected (meta)materials have been extensively studied over the past decade, but their dynamic responses, especially in acoustic metamaterials with engineered wave propagation behavior, represent a new frontier. However, challenges in miniaturizing and characterizing acoustic metamaterials in high-frequency (megahertz) regimes have hindered progress toward experimentally implementing ultrasonic-wave control. Here, we present an inertia design framework based on positioning microspheres to tune responses of 3D microscale metamaterials. We demonstrate tunable quasi-static stiffness by up to 75% and dynamic longitudinal-wave velocities by up to 25% while maintaining identical material density. Using noncontact laser-based dynamic experiments of tunable elastodynamic properties and numerical demonstrations of spatio-temporal ultrasound wave propagation, we explore the tunable static and elastodynamic property relation. This design framework expands the quasi-static and dynamic metamaterial property space through simple geometric changes, enabling facile design and fabrication of metamaterials for applications in medical ultrasound and analog computing.

42 ENGINEERING↗

Probing the Mechanical Performance of Micro-architected Porous Structures Through In Situ Characterization and Analysis

Micropores play critical roles in both natural and man-made materials. Such pores take on a variety of shapes and sizes ranging from spherical to irregular sphere-like voids with diameters spanning from the nanometer to millimeter scales. When porous structures are mechanically loaded, the pores direct the stress around their free surfaces, altering the material’s mechanical response relative to fully dense materials. In this study, for the first time, we create micro-architected porous samples using nanolithography and investigate the role of pore morphology by conducting a series of in situ micropillar compression tests in scanning electron microscopy. The findings demonstrate that porosity is the primary factor influencing the mechanical response of these micro-architected materials, as often seen on a macroscopic level. Additionally, we observed that pore geometry had a significant impact on Young’s modulus, yield stress, and strain energy density as a secondary parameter. Then, the extracted Young’s modulus was compared to macroscopic empirical models and determined the analytical models sufficiently described the impact of porosity in the microscopic scale but failed to capture the impact of second-order parameters. Furthermore, these results suggest how porous materials can be tailored to achieve desired mechanical properties based on the engineering applications of interest.

36 MATERIALS SCIENCE↗

Additive manufacturing of hierarchical three- dimensional micro-architected aerogels

Disclosed here is a method for making a three-dimensional micro-architected aerogel, comprising: (a) curing a reaction mixture comprising a co-sol-gel material (e.g., graphene oxide (GO)) and at least one catalyst to obtain a crosslinked co-sol-gel (e.g., GO hydrogel); (b) providing a photoresin comprising a solvent, a photoinitiator, a crosslinkable polymer precursor, and a dispersion of the crosslinked co-sol-gel (e.g., GO hydrogel); (c) curing the photoresin using projection microstereolithography layer-by-layer to produce a wet gel having a pre-designed three-dimensional structure; (d) drying the wet gel to produce a dry gel; and (e) pyrolyzing the dry gel to produce a three-dimensional micro-architected aerogel (e.g., graphene aerogel). Also disclosed is a photoresin for projection microstereolithography, comprising a solvent, a photoinitiator, a crosslinkable polymer precursor, and a dispersion of a crosslinked co-sol-gel.

Worsley, Marcus A.↗

Investigating property-porosity relationships for micro-architected lattice structures

Micro-architected structures are increasingly valued for their light weight and tunable mechanical properties; this class of material includes sheet structures like the Schöen gyroid and beam lattices like the octet. For design purposes, it is critical to understand how to tune the relative density (RD) to obtain desired mechanical properties. This study investigates the mechanical response of Ti-6Al-4V gyroid structures, spanning a broad range of RDs (0.03–0.90), unit cell sizes (1–4 cm), and sheet thicknesses (0.2–7.8 mm). Results demonstrate that the classical Gibson-Ashby power law scaling between RD and modulus and yield stress does not adequately capture the response over a wide range of RDs, nor does it extrapolate correctly to the fully dense solid. Analytical models, in concert with experimental results and high-fidelity finite element calculations, show that the deviation from Gibson-Ashby reflects a transition from structure-dominated to material-dominated behavior. Distinctions are drawn between scaling relationships and property-porosity models, and an analytical model is proposed to better capture the evolution of mechanical properties with RD. These observations are mirrored in other architected topologies, like the octet, and highlight the importance of understanding the relationship between mechanical properties and geometry for design purposes.

Materials science↗

Mechanical Consequences of Oxygen Inhibition in Vat Polymerization

Vat polymerization is a type of additive manufacturing that is used extensively to produce micro-architected structures for mechanical applications, which brings the mechanical properties of photopolymerized resins into sharp focus. However, it is known that photopolymerization is sensitive to a number of factors, perhaps the most notorious of which is oxygen inhibition. Herein, the degree to which oxygen inhibition influences the macroscopic and microscopic properties of structures made using vat polymerization is explored. This work is motivated by an observation of lattices being >4 times softer in the experiment than predicted by simulation, which is hypothesized to be due to the material at the surface being incompletely cured. Furthermore, this hypothesis is supported by four-point bending tests in which flexural modulus is found to increase with beam thickness. Nanoindentation and bulk compression studies show that this surface softening is present for three distinct resins. Importantly, it is observed that structures post-print cured in nitrogen are stiffer than those post-print cured in air, however, regardless of the post-print curing environment, printing samples in the presence of oxygen makes them softer than samples photocured in nitrogen. Collectively, these results show the outsized influence of oxygen inhibition on micro-architected structures realized using vat polymerization.

36 MATERIALS SCIENCE↗

A linked-scale coupled model of mass erosion and redistribution in plasma-exposed micro-foam surfaces

Surface evolution due to exposure to harsh environments is of importance in many scientific and technological applications. In plasma-exposed materials, the surface receives charged particles from the plasma, leading to a series of processes that drive the system far from equilibrium and may lead to the severe deterioration of the surface properties. Although surface morphological changes are driven by atomic collisions taking place over picoseconds and nanometers, these processes result in mass loss and redistribution of matter over much larger length and time scales. This necessitates a multi-scale approach capable of capturing the range of processes linking primary atomic collision events with engineering-level surface geometry changes. In this paper, we develop a computational model to simulate the morphological evolution and effective erosion rate of micro-architected tungsten foams during low-energy plasma ion bombardment. Furthermore, the model acts on several length scales, with the energy and angular dependence of the sputtering yield of flat tungsten surfaces determined using the SRIM code based on the binary collision approximation. This information is introduced into a low-fluence, short-term Monte Carlo raytracing model, and further into a high-fluence, long-term particle transport model. In the latter, material particles representing billions of atoms are described in a digitized 3-D representation of the foam structure from X-ray tomography data, and are sputtered off and redeposited using the atomistic information. We show that the redeposition of sputtered atoms leads to partial self-healing in the bottom layers with a sharp reduction in the sputtering coefficient of low density foams, roughly 25% of the solid W value. This is in qualitative agreement with recent experiments on low porosity W structures. At high fluence, the foam structure degrades considerably as there are fewer ligaments available to recapture sputtered atoms and, consequently, the sputtering rate increases again.

36 MATERIALS SCIENCE↗

Quantum Sensing in Micro-Architected Scaffolds

Quantum sensing with nitrogen-vacancy centers in diamond has emerged as a powerful tool for measuring diverse physical parameters, yet the versatility of these measurement approaches is often limited by the achievable layout and dimensionality of bulk-crystal platforms. Here, in this study, we demonstrate a versatile approach to creating designer quantum sensors by surface-functionalizing multiphoton lithography microstructures with NV-containing nanodiamonds. We showcase this capability by fabricating a 150 μm × 150 μm × 150 μm triply periodic minimal surface gyroid structure with millions of attached nanodiamonds. We demonstrate a means to volumetrically image these structures using a refractive index matching confocal imaging technique and extract ODMR spectra from 1.86 μm × 1.86 μm areas of highly concentrated nanodiamonds across a cross-section of the gyroid. Furthermore, the high density of sensing elements enables ensemble temperature measurements with a sensitivity of 0.548 ± 0.084 K/√Hz at 5 mW excitation power. This approach to creating quantum-enabled microarchitectures opens new possibilities for multimodal sensing in complex three-dimensional environments.

Materials science↗