The present article addresses design of stiff, elastically isotropic trusses and their mechanical properties. Isotropic trusses are created by combining two or more elementary cubic trusses in appropriate proportions and with their respective nodes lying on a common space lattice. Two isotropic binary compound trusses and many isotropic ternary trusses are identified, all with Young’s moduli equal to the maximal possible value for isotropic strut-based structures. In finite-sized trusses, strain elevations are obtained in struts near the external free boundaries: a consequence of reduced nodal connectivity and thus reduced constraint on strut deformation and rotation. Although the boundary effects persist over distances of only about two unit cell lengths and have minimal effect on elastic properties, their manifestations in failure are more nuanced, especially when failure occurs by modes other than buckling (yielding or fracture). Exhaustive analyses are performed to glean insights into the mechanics of failure of such trusses.

New closed-form analytical equations for volume fractions and surface-area-to-volume ratios for architected lattice cellular materials are derived. Prior approximate equations which erroneously over count overlapping volumes and the associated surface area are commonly used in the literature. These equations are found to have up to 184% error for volume fraction calculations for hollow lattices and 211% error for surface-area-to-volume ratio calculations, thus necessitating computational methods to arrive at accurate geometric properties for cellular lattice materials. This work derives new equations which are accurate to better than 1% for both volume fraction and surface-area-to-volume ratio as compared to the computational models. These new equations for cellular lattice materials are applicable to both pyramidal and tetrahedral unit cells as well as to both hollow and solid lattice members. By eliminating the need for numerical models to compute accurate volume fractions and surface-area-to-volume ratios of architected cellular materials, these new analytical equations will enable accurate yet computationally efficient optimization of the physical properties of architected cellular materials.

Specifically designed microlattices are able to combine outstanding mechanical and physical properties and, thus, expand the actual limits of the material property space. However, post-yield softening induced by plastic buckling or crushing of individual ligaments limits performance under cyclic loading, which affects their energy absorption capabilities. Understanding deformation under repeated loading is key to further optimizing these high-strength materials. While until now mainly hollow metallic microlattices and multistable or tailored buckling structures have been analyzed, this study investigates deformation and failure of polymer and ceramic-polymer microlattices under cyclic loading to understand the (i) influence of the microarchitecture and (ii) influence of processing conditions on the energy absorption capability. Despite fracture of individual struts, the stretching-dominated microarchitectures possess a superior behavior especially for larger cycle numbers. In combination with a specific annealing treatment of the polymer material, high recoverability and energy dissipation can be achieved.

Negative stiffness honeycombs are architected metamaterials that utilize elastic buckling to absorb mechanical energy. Relative to conventional honeycomb materials, they offer several advantages, including the ability to recover their initial configuration and offer consistently repeatable mechanical energy absorption. In this paper, fully recoverable negative stiffness honeycombs are fabricated from thermoplastic and metallic parent materials. The honeycombs are subjected to quasistatic and impact loading to demonstrate the predictability and repeatability of their energy absorption characteristics across a variety of loading conditions. Results indicate that these honeycombs offer nearly ideal shock isolation by thresholding the acceleration of an isolated mass at a predetermined level and that this thresholding behavior is highly repeatable as long as the magnitude of the mechanical energy imparted to the system does not exceed the energy absorption capacity of the honeycomb.

Bistable Auxetic Metamaterials (BAMs) are a class of monolithic perforated periodic structures with negative Poisson’s ratio. Under tension, a BAM can expand and reach a second state of equilibrium through a globally large shape transformation that is ensured by the flexibility of its elastomeric base material. However, if made from a rigid polymer, or metal, BAM ceases to function due to the inevitable rupture of its ligaments. The goal of this work is to extend the unique functionality of the original kirigami architecture of BAM to a rigid solid base material. We use experiments and numerical simulations to assess performance, bistability, and durability of rigid BAMs at 10,000 cycles. Geometric maps are presented to elucidate the role of the main descriptors of the BAM architecture. The proposed design enables the realization of BAM from a large palette of materials, including elastic-perfectly plastic materials and potentially brittle materials.

Direct ink writing of silicone elastomers enables printing with precise control of porosity and mechanical properties of ordered cellular solids, suitable for shock absorption and stress mitigation applications. With the ability to manipulate structure and feedstock stiffness, the design space becomes challenging to parse to obtain a solution producing a desired mechanical response. Here, we derive an analytical design approach for a specific architecture. Results from finite element simulations and quasi-static mechanical tests of two different parallel strand architectures were analyzed to understand the structure-property relationships under uniaxial compression. Combining effective stiffness-density scaling with least squares optimization of the stress responses yielded general response curves parameterized by resin modulus and strand spacing. An analytical expression of these curves serves as a reduced order model, which, when optimized, provides a rapid design capability for filament-based 3D printed structures. As a demonstration, the optimal design of a face-centered tetragonal architecture is computed that satisfies prescribed minimum and maximum load constraints.

The indentation response of a 3D noninterlaced composite comprising three sets of orthogonal carbon-fibre tows in an epoxy matrix is investigated. The 3D composites have a near isotropic and ductile indentation response. The deformation mode includes the formation of multiple kinks in the tows aligned with the indentation direction and shearing of the orthogonally oriented tows. Finite element (FE) calculations are also reported wherein tows in one direction are explicitly modeled with the other two sets of orthogonal tows and the matrix pockets treated as an effective homogenous medium. The calculations capture the indentation response in the direction of the explicitly modeled tows with excellent fidelity but under-predict the indentation strength in the other directions. In contrast to anisotropic and brittle laminated composites, 3D noninterlaced composites have a near isotropic and ductile indentation response making them strong candidates for application as materials to resist impact loading.

Introducing architected cuts is an attractive and simple approach to tune mechanical behaviors of planar materials like thin films for desirable or enhanced mechanical performance. However, little has been studied on the effects of architected cuts on functional materials like piezoelectric materials. We investigated how architected cut patterns affect mechanical and piezoelectric properties of polyvinylidene fluoride thin films by numerical, experimental, and analytical studies. Our results show that thin films with architected cuts can provide desired mechanical features like enhanced compliance, stretchability, and controllable Poisson’s ratio and resonance frequency, while maintaining piezoelectric performance under static loadings. Moreover, we could observe maximum ∼30% improvement in piezoelectric conversion efficiency under dynamic loadings and harvest energy from low frequency (<100 Hz) mechanical signals or low velocity (<5 m/s) winds, which are commonly existing in ambient environment. Using architected cuts doesn't require changing the material or overall dimensions, making it attractive for applications in self-powered devices with design constraints.

Architected materials are materials engineered to utilize their topological aspects to enhance the related physical and mechanical properties. With the witnessed progressive advancements in fabrication techniques, obstacles and challenges experienced in manufacturing geometrically complex architected materials are mitigated. Different strut-based architected lattice structures have been investigated for their topology-property relationship. However, the focus on lattice design has recently shifted toward structures with mathematically defined architectures. In this work, we investigate the architecture-property relationship associated with the possible configurations of employing the mathematically attained Schoen's I-WP (IWP) minimal surface to create lattice structures. Results of mechanical testing showed that sheet-based IWP lattice structures exhibit a stretching-dominated behavior with the highest structural efficiency as compared to other forms of strut-based and skeletal-based lattice structures. This study presents experimental and computational evidence of the robustness and suitability of sheet-based IWP structures for different engineering applications, where strong and lightweight materials with exceptional energy absorption capabilities are required.

3D microarchitected metamaterials exhibit unique, desirable properties influenced by their small length scales and architected layout, unachievable by their solid counterparts and random cellular configurations. However, few of them can be used in high-temperature applications, which could benefit significantly from their ultra-lightweight, ultrastiff properties. Existing high-temperature ceramic materials are often heavy and difficult to process into complex, microscale features. Inspired by this limitation, we fabricated polymer-derived ceramic metamaterials with controlled solid strut size varying from 10-µm scale to a few millimeters with relative densities ranging from as low as 1 to 22%. We found that these high-temperature architected ceramics of identical 3D topologies exhibit size-dependent strength influenced by both strut diameter and strut length. Weibull theory is utilized to map this dependency with varying single strut volumes. These observations demonstrate the structural benefits of increasing feature resolution in additive manufacturing of ceramic materials. Through capitalizing upon the reduction of unit strut volumes within the architecture, high-temperature ceramics could achieve high specific strength with only fraction of the weight of their solid counterparts.