Micro-architectured Materials Research Articles

Flexural Properties of Additively Manufactured Structures Reinforced with Cellular and Fractal Patterns

The interest in exploring new microarchitected materials that take advantage of precise geometrical construction to achieve unique properties has recently arisen due to the accelerated development of additive manufacturing. Exploring and understanding the mechanical behavior of additively manufactured structures remains crucial to expand the capabilities of this technology. Herein, a methodology to design, fabricate, and characterize the flexural behavior of additively manufactured structures reinforced with cellular and fractal patterns is presented. A total of 16 different arrangements are designed, tested, and numerically simulated, including 4 cellular arrangements, 10 fractal, and 2 nonreinforced structures. Samples are fabricated out of polylactic acid via material extrusion, subjected to three‐point bending loading and simulated via finite element models. Further, the fracture modes and deformation mechanisms from the experimental tests to obtain a broad overview of their flexural capabilities are examined. An increase in stiffness of up to 36% is observed for the cellular‐reinforced structures, while the fractal‐reinforced structures present great recovery, flexibility, and unconventional bending behaviors.

Decoupling particle-impact dissipation mechanisms in 3D architected materials

Ultralight architected materials enabled by advanced manufacturing processes have achieved density-normalized strength and stiffness properties that are inaccessible to bulk materials. However, the majority of this work has focused on static loading and elastic-wave propagation. Fundamental understanding of the mechanical behavior of architected materials under large-deformation dynamic conditions remains limited, due to the complexity of mechanical responses and shortcomings of characterization methods. Here, we present a microscale suspended-plate impact testing framework for three-dimensional micro-architected materials, where supersonic microparticles to velocities of up to 850 m/s are accelerated against a substrate-decoupled architected material to quantify its energy dissipation characteristics. Using ultra-high-speed imaging, we perform in situ quantification of the impact energetics on two types of architected materials as well as their constituent nonarchitected monolithic polymer, indicating a 47% or greater increase in mass-normalized energy dissipation under a given impact condition through use of architecture. Post-mortem characterization, supported by a series of quasi-static experiments and high-fidelity simulations, shed light on two coupled mechanisms of energy dissipation: material compaction and particle-induced fracture. Together, experiments and simulations indicate that architecture-specific resistance to compaction and fracture can explain a difference in dynamic impact response across architectures. We complement our experimental and numerical efforts with dimensional analysis which provides a predictive framework for kinetic-energy absorption as a function of material parameters and impact conditions. We envision that enhanced understanding of energy dissipation mechanisms in architected materials will serve to define design considerations toward the creation of lightweight impact-mitigating materials for protective applications.

A micro-architectured material as a pressure vessel for green mobility

A shellular is a micro-architectured material, composed of a continuous smooth-curved thin shell in the form of a triply periodic minimal surface. Thanks to the unique geometry, a shellular can support external load by co-planar stresses, unlike microlattice, nanolattice, and mechanical metamaterial. That is, the shellular is the only stretching-dominated material with the highest strength at a density of less than 10−2 g/cc. Therefore, it is expected to support internal pressure, too, by the bi-axial tensile stresses like a balloon. For more than 300 years, spherical and cylindrical vessels have been viable yet compromised options for storing pressurized gases. However, emerging green mobility necessitates a safer and more spatially conformable storage solution for hydrogen than spherical and cylindrical vessels these conventional vessels. In this study, we propose to use the shellular as a pressure vessel. Due to the distinct topological nature – periodic micro-cells constituting the triply periodic minimal surface, the alternative pressure vessel can be tailored individually for spatial requirements while ensuring safety with leak-before-break. For a given constituent material and prescribed pressure, the achievable internal volume-per-total weight of a P-surfaced, cold-stretched, double-chambered shellular vessel with a number of cells more than 15 × 15 × 15 can exceed the practical upper bound of both spherical and cylindrical vessels. For the applications, a thin shell with the large surface area of this micro-architecture is ideal for interfacial transfer of heat or mass between its two sub-volumes under internal pressure.

Lightweighting structures using an explicit microarchitectured material framework

In this paper, a new approach to design ultralight structures is developed based on a previous work called Efficient Multiscale Topology Optimization. A parameterized (or explicit) truss-based cell is introduced to generate intrinsically well-connected microstructures and to get clear interpretable optimal multiscale structures. The method uses a pre-computed database of optimal micro-cells to be computational efficient without losing in structural performances. The parameterization allows to generate a lightweight database just storing the set of parameters, that define the optimal cells, and the cells properties, that are obtained through inverse homogenization. The method has been successfully tested on two-dimensional compliance problems. Several examples demonstrate its versatility and give quantitative results. Moreover, it allows to obtain structures compatible with additive manufacturing processes, to naturally solve concurrent multi-scale problems, as well as controlled porosity and optimal fiber orientation problems.

CO_2 footprint minimization of solar-powered HALE using MDO and eco-material selection

Multidisciplinary Design Optimization (MDO) enables one to reach a better solution than by optimizing each discipline independently. In particular, the optimal structure of a drone varies depending on the selected material. The CO_2 footprint of a solar-powered High Altitude Long Endurance (HALE) drone is optimized here, where the structural materials used is one of the design variables. Optimization is performed using a modified version of OpenAeroStruct, a framework based on OpenMDAO. Our EcoHale framework is validated on a classical HALE testcase in the MDO community (FBhale) constructed using high-fidelity codes compared to our low-fidelity approach. The originality of our work is to include two specific disciplines (energy and environment) to adapt to a new problem of CO_2 minimization. The choice of eco-materials is performed in the global MDO loop from a choice of discrete materials . This is achieved through a variable relaxation, enabling the use of continuous optimization algorithms inspired from multimaterial topology optimization. Our results show that, in our specific case of electric drone, the optimal material in terms of CO_2 footprint is also the optimal material in terms of weight. It opens the door to new researches on digital microarchitectured materials that will decrease the CO_2 footprint of the drone.

Knots are not for naught: Design, properties, and topology of hierarchical intertwined microarchitected materials.

Lightweight and tough engineered materials are often designed with three-dimensional hierarchy and interconnected structural members whose junctions are detrimental to their performance because they serve as stress concentrations for damage accumulation and lower mechanical resilience. We introduce a previously unexplored class of architected materials, whose components are interwoven and contain no junctions, and incorporate micro-knots as building blocks within these hierarchical networks. Tensile experiments, which show close quantitative agreements with an analytical model for overhand knots, reveal that knot topology allows a new regime of deformation capable of shape retention, leading to a ~92% increase in absorbed energy and an up to ~107% increase in failure strain compared to woven structures, along with an up to ~11% increase in specific energy density compared to topologically similar monolithic lattices. Our exploration unlocks knotting and frictional contact to create highly extensible low-density materials with tunable shape reconfiguration and energy absorption capabilities.

Data assisted framework for topology design of micro-architected compliant mechanisms

A computational multiscale design of micro-architected compliant mechanisms is presented. The optimal design is performed with spatially varying material properties at the macro scale where the homogenized stiffness tensor is considered as the design variable (free material optimization). Mapping the obtained spatially-varying properties onto micro-architected materials is achieved using inverse design topology optimization. The originality of this work lies in using a database assisted framework in order to obtain the optimal design. Two approaches are compared: the first one does not make use of the database wheres the second approach is driven by an adequate material database. For the first approach, the required materials are constructed a posteriori while the materials are constructed a priori and stored in a catalog for the second approach. This catalog is then exploited during the macro-optimization. The performances of both methods is compared via different examples that highlight the advantages of the database strategy in terms of the required micro-architected materials feasibility.

Level set-based topological design of multiphase micro-architectured materials using alternating active-phase method

Micro-architectured materials with periodically configured microstructures are widely used in various engineering fields due to their superior mechanical properties. Compared with conventional topology design with one single material, topological design with multiple materials can provide a better solution as the expanded design freedom. This paper presents a level set-based multi-material topological design method for micro-architectured materials involving three phases or more. In this method, a difference-set-based multi-material level set model is employed to represent the topology of each phase, in which N + 1 phases can be precisely represented by the sequential difference-set of N level set functions without any overlaps and redundant regions. By using an alternating active-phase algorithm, the multi-material topology design problem with N + 1 phases is splitted into N(N + 1)/2 binary-phase topological design sub-problems, where each sub-problem involves fewer design variables and volume constraints. The effective properties of multiphase micro-architectured materials are evaluated by a numerical homogenization approach, and their topological evolutions of two active phases in each sub-problem can be readily achieved by updating a single level set function, which greatly facilitate the extension to topological design problems with more phases. Both numerical examples and additive-manufactured specimens demonstrate the effectiveness of the proposed method for designing multiphase micro-architectured materials.

Nonlinear coarse-graining models for 3D printed multi-material biomimetic composites

Bio-inspired composites are a great promise for mimicking the extraordinary and highly efficient properties of natural materials. Recent developments in voxel-by-voxel 3D printing have enabled extreme levels of control over the material deposition, yielding complex micro-architected materials. However, spatial complexity makes it a formidable challenge to find the optimal distribution of both hard and soft phases. To address this, a nonlinear coarse-graining approach is developed, where foam-based constitutive equations are used to predict the mechanics of biomimetic composites. The proposed approach is validated by comparing coarse-grained finite element predictions against full-field strain distributions measured using digital image correlation. To evaluate the degree of coarse-graining on model accuracy, pre-notched specimens decorated with a binarized version of a renowned painting were modeled. Subsequently, coarse-graining is used to predict the fracture behavior of bio-inspired composites incorporating complex designs, such as functional gradients and hierarchical organizations. Finally, as a showcase of the proposed approach, the inverse coarse-graining is combined with a theoretical model of bone tissue adaptation to optimize the microarchitecture of a 3D-printed femur. The predicted properties were in exceptionally good agreement with the corresponding experimental results. Therefore, the coarse-graining method allows the design of advanced architected materials with tunable and predictable properties.

Hydrogen embrittlement in micro-architectured materials

Hydrogen embrittlement is a classical problem in bulk materials while it is rather untouched for advanced materials such as micro-architectured materials. This can be a barrier to industrial adoption of these materials where hydrogen is present as a popular source of energy. In this study, we developed a numerical scheme to assess the hydrogen degradation in metallic micro-architectured materials. The numerical scheme is built on the concept of elastoplastic homogenization and two hydrogen embrittlement theories, i.e. hydrogen enhanced decohesion (HEDE) and hydrogen enhanced localized plasticity (HELP). The use of homogenization allows for explicit definition of a unit-cell, drastically improving the computation time. The hydrogen degradation loci of two specific micro-architectured materials, that is cubic (with 10%, 20% and 30% relative densities) and body-center cubic (with 20% relative density), are numerically characterized. Additionally, the influence of unit-cell topology, relative density, and trap hydrogen on the degradation of homogenized macroscopic material is determined. Finally, a unique failure locus is provided for generic cubic unit-cell with arbitrary relative densities. This degradation law is independent of the relative density and can be interpreted as a material property, contributing to the material design charts.

Damage tolerance in additively manufactured ceramic architected materials

Technical ceramics exhibit exceptional high-temperature properties, but unfortunately their extreme crack sensitivity and high melting point make it challenging to manufacture geometrically complex structures with sufficient strength and toughness. Emerging additive manufacturing technologies enable the fabrication of large-scale complex-shape artifacts with architected internal topology; when such topology can be arranged at the microscale, the defect population can be controlled, thus improving the strength of the material. Here, ceramic micro-architected materials are fabricated using direct ink writing (DIW) of an alumina nanoparticle-loaded ink, followed by sintering. After characterizing the rheology of the ink and extracting optimal processing parameters, the microstructure of the sintered structures is investigated to assess composition, density, grain size and defect population. Mechanical experiments reveal that woodpile architected materials with relative densities of 0.38–0.73 exhibit higher strength and damage tolerance than fully dense ceramics printed under identical conditions, an intriguing feature that can be attributed to topological toughening.

Multi-objective design optimization of 3D micro-architected implants

Recent advances in 3D printable micro-architected materials offer unprecedented possibilities for the development of highly tailored orthopaedic implants. These devices, which are typically made from fully solid materials, significantly alter load transmission to the surrounding bone tissue, potentially leading to interface instability and bone resorption. In this work, we present computational methods to synthesize three dimensional (3D), patient-specific, implants with heterogeneous micro-architecture. Our method simultaneously minimizes the risks of load-induced interface fracture and peri-prosthetic bone remodelling, while taking into account functional and manufacturing constraints.We first develop a novel parametric micro-architecture with desirable functional attributes and a wide range of effective mechanical properties, including both positive and negative Poisson’s ratios. We then present formulations which optimize the spatial configuration of micro-architecture parameters in order to simultaneously minimize the risk of load-induced interface fracture and post-operative bone remodelling. To that end, a novel bone remodelling objective is devised, taking into account both bone apposition and resorption, predicted via a model based on strain–energy density. The interface fracture objective is defined as the maximum value of the multi-axial Hoffman failure criterion along the interface.The procedure is applied to the design of 3D titanium hip implants with prescribed conventional geometries and compared, in silico, to both a conventional solid implant and a homogeneous low-stiffness lattice design. The optimized implant results in a performance improvement of 64.0% in terms of bone remodelling, and 13.2% in terms of interface fracture risk, compared to a conventional solid implant design.

Anisotropic yield models for lattice unit cell structures exploiting orthotropic symmetry

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%.

The coupled strength and toughness of interconnected and interpenetrating multi-material gyroids

The growth of additive manufacturing technologies has spurred interest in examining multi-material micro-architected materials for filling the so-called white spaces in the Ashby strength versus toughness plots. We investigate this problem using interconnected and interpenetrating double gyroids comprising ductile and brittle phases as an exemplar. Both strength and toughness at the initiation of crack growth are shown to vary non-monotonically with the volume fraction of the two phases and multi-material double gyroids significantly outperform their single material counterparts. However, we establish that at a given relative density, the strength and toughness cannot be simultaneously enhanced for architecture designs, which include varying gyroid orientations, phase volume fractions, and the unit cell length scales of the two phases. Intriguingly, even crack flank bridging by the ductile phase during crack growth is insufficient to overcome this inherent property of the interpenetrating gyroids. Our conclusion is that multi-material interpenetrating micro-architected solids are unlikely to outperform single material non-interpenetrating lattices from a strength–toughness perspective but rather become optimal when multi-functionality is required.Impact statementThe integration of materials and architectural features at multiple scales into structural mechanics gave us structural designs such as the Eiffel Tower. The explosion of additive manufacturing methods has opened new avenues for the invention of multi-material micro-architected materials that simultaneously possess high strength and toughness at a low density, and thereby can fill the so-called “white spaces” in the Ashby strength–toughness space. The idea is to construct three-dimensional materials with a network of crack arrestors like in rip-stop nylon and break the link between toughness and strength. We use interconnected and interpenetrating double gyroids comprising ductile and brittle phases as an exemplar to investigate the opportunities of such designs. Intriguingly, from a perspective based solely on strength and toughness, we show that multi-material micro-architectures cannot outperform their single material counterparts at a given relative density. In fact, in most designs the coupling between the two phases is non-synergistic. Rather, we argue that multi-material designs such as those used in rip-stop nylon are driven by multi-functional considerations beyond mechanical properties.Graphical abstract

A porosity-based model of dynamic compaction in under-dense materials

Under-dense metals including micro-architectured structures and stochastic foams provide a combination of low weight, high strength-to-weight ratio, high permeability, and low stiffness, which make them desirable materials for a variety of applications. Specifically, their energy absorption capabilities under dynamic compressive loads are desirable. However, under high loading rates there are several challenges in performing accurate simulations of under-dense materials—primarily, the responses of materials with high, low, and zero porosity are difficult to accurately predict with a single model. A general model that tracks porosity and pore geometry and is flexible for a variety of matrix material constitutive responses has yet to be produced. This work outlines such a model and applies it to high loading rate simulations that demonstrate the model’s ability to address a variety of stress states. The approach is to extend a porosity model meant for isolated porosity of low-to-modest volume fraction to the application space of under-dense materials. Calibration parameters are used to account for complex mechanisms as well as the effects of the geometries of various under-dense materials. This results in a general, versatile, and flexible model. A study of the model’s sensitivity to calibration parameters is shown along with qualitative and quantitative comparisons to direct numerical simulations (DNS) and predictions resulting from impact velocities and flyer structures for which the model is not calibrated. This model can simulate a range of compaction conditions and is less computationally intense than direct numerical simulations which gives it utility in the design of micro-architected materials for impact mitigation, energy absorption, and other applications.

Merging strut-based and minimal surface meta-biomaterials: Decoupling surface area from mechanical properties

The rational design of bone-substituting biomaterials is relatively complex because they should meet a long list of requirements for optimal performance. Meta-biomaterials are micro-architected materials that hold great promise for meeting those requirements as they offer a unique combination of mechanical, mass-transport, and biological properties. There are, however, inherent couplings between the different types of properties of many such materials that make it impossible to simultaneously achieve all the design criteria. An example of such a coupling exists between the mechanical properties and the surface area. Strut-based, metallic meta-biomaterials are known to offer bone-mimicking mechanical properties, but they have limited surface area for cell adherence. Increasing the surface generally results in an undesirable increase in the mechanical properties that could lead to stress shielding. Here, we combine strut-based lattices with minimal surfaces to decouple these two properties. We added minimal surface patches to the designs of both auxetic and non-auxetic meta-biomaterials while minimizing their contribution to the mechanical properties of the resulting meta-biomaterials through the rational application of cuts or “slits”. All designs were additively manufactured using selective laser melting and mechanically tested to obtain their quasi-static mechanical properties, including their Poisson’s ratio, in two configurations. A finite element-based computational homogenization code was used to compute the elastic moduli and anisotropy of the structures. The results show that the minimal surface patches substantially increase the available surface area without significantly affecting the mechanical properties. Without the slits, the surfaces significantly affected the elastic modulus and deformation behavior of the meta-biomaterials. A similar strategy could be used to tune the biodegradation rate of biodegradable metals and the permeability of meta-biomaterials in general.

Computational model for low cycle fatigue analysis of lattice materials: Incorporating theory of critical distance with elastoplastic homogenization

A novel numerical framework for low cycle fatigue analysis of lattice materials is presented. The framework is based on computational elastoplastic homogenization equipped with the theory of critical distance to address the fatigue phenomenon. Explicit description of representative volume element and periodic boundary conditions are combined for computational efficiency and elimination of the boundary effects. The proposed method is generic and applicable to periodic micro-architectured materials. The method has been applied to 2-D auxetic and 3-D kelvin lattices. The classical Coffin-Manson and Morrow models are used to provide fatigue life predictions (strain-life curves). Predicted fatigue lives for the auxetic lattice are shown to provide good correspondence to experimentally found fatigue lives from the literature.

A compliant and low-expansion 2-phase micro-architectured material, with potential application to solid-state Li-ion batteries

A two-phase 2D lattice material is identified that possesses both a high macroscopic compliance and a low macroscopic coefficient of thermal expansion. The macroscopic effective properties of the lattice are analysed and the features that give high macroscopic compliance and low macroscopic actuation strain are identified. A detailed case study is presented to explore the potential of the lattice for use as a composite cathode in a solid-state Li-ion battery, taking into account the swelling of the active cathode material upon lithiation. A design map is developed to reveal the competition between battery capacity and degradation due to fracture of the composite cathode. The intent is to identify promising battery topologies and compositions by overcoming the usual problems associated with cathode swell during charge and discharge.

Multiscale topology optimization of 3D structures: A micro-architectured materials database assisted strategy

This article presents a datadriven multiscale optimization method for solving 3D problems under given boundary conditions. The topology is represented by an extended level-set function that allows the nucleation of new holes throughout the process making it less sensitive to the initial guess. The two scales involved are the structural (macro) scale and the material (micro) scale. For the macro scale, the stiffness is maximized while reducing the weight of the structure; while for the micro scale, the homogenized elasticity tensor is prescribed and the weight is also minimized. In order to decrease the significant computational cost of multi-scale optimization, a datadriven approach is proposed. The method consists in two main steps: (1) an offline step to build a database (catalog of optimal micro-architectured materials indexed by their effective elasticity) for a wide range of desired elasticity tensors, and (2) an online step aiming to optimize the 3D structure at the macroscale. The precomputed catalog is thus interrogated in order to find the best micro-architectured material within the macroscale optimization. This method performs a two scales weight minimization and leads to a significantly light structure design. The optimization formulation is first introduced. Then a few 3D benchmark tests are given for the multi-scale optimization using micro-architectured materials.

Architected material analogs for shape memory alloys

Architected material analogs for shape memory alloys