Practical applications of mechanical metamaterials often involve solving inverse problems aimed at finding microarchitectures that give rise to certain properties. The limited resolution of additive manufacturing techniques often requires solving such inverse problems for specific specimen sizes. Moreover, the candidate microarchitectures should be resistant to fatigue and fracture. Such a multi-objective inverse design problem is formidably difficult to solve but its solution is the key to real-world applications of mechanical metamaterials. Here, a modular approach titled “Deep-DRAM” that combines four decoupled models is proposed, including two deep learning (DL) models, a deep generative model based on conditional variational autoencoders, and direct finite element (FE) simulations. Deep-DRAM integrates these models into a framework capable of finding many solutions to the posed multi-objective inverse design problem based on random-network unit cells. Using an extensive set of simulations as well as experiments performed on 3D printed specimens, it is demonstrate that: 1) the predictions of the DL models are in agreement with FE simulations and experimental observations, 2) an enlarged envelope of achievable elastic properties (e.g., rare combinations of double auxeticity and high stiffness) is realized using the proposed approach, and 3) Deep-DRAM can provide many solutions to the considered multi-objective inverse design problem.

Background: Nuclear factor erythroid 2–related factor 2 (Nrf2) is a crucial transcription factor for cellular redox homeostasis. The association of Nrf2 with elderly female osteoporotic has yet to be fully described. The aim was to elucidate a potential age-dependent Nrf2 contribution to female osteoporosis in mice. Methods: Eighteen female wild type (WT) and 16 Nrf2-knockout (KO) mice were sacrificed at different ages (12 weeks = young mature adult and 90 weeks = old) to analyze their femurs. The morphological properties (trabecular and cortical) were evaluated by micro-computed tomography (μCT) and compared to gold standard histochemistry analysis. The quasi-static compression tests were performed to calculate the mechanical properties of bones. Additionally, the population of bone resorbing cells and aromatase expression by osteocytes was immunohistochemically evaluated and empty osteocyte lacunae was counted in cortical bone. Results: Old Nrf2-KO mice revealed a significantly reduced trabecular bone mineral density (BMD), cortical thickness, cortical area, and bone fraction compared to old WT mice, regardless of no significant difference in skeletally mature young adult mice between WT and KO. Specifically, while all old WT mice showed thin metaphyseal trabeculae, trabecular bone was completely absent in 60% of old KO mice. Additionally, old KO mice showed significantly more osteoclast-like cells and fewer aromatase-positive osteocytes than WT mice, whereas the occurrence of empty osteocyte lacunae did not differ between both groups. Nrf2-KO mice further showed an age-dependently reduced fracture resilience compared to age-matched WT mice. Conclusion: Our results suggest that chronic Nrf2 loss can lead to age-dependent progression of female osteoporosis.

Emerging multi-material 3D printing techniques enables the rational design of metamaterials with not only complex geometries but also arbitrary distributions of multiple materials within those geometries, yielding unique combinations of elastic properties. However, discovering the rare designs that lead to highly unusual combinations of material properties, such as double-auxeticity and high elastic moduli, remains a non-trivial crucial task. Here, we use computational models and deep learning algorithms to identify rare-event designs. In particular, we study the relationship between random distributions of hard and soft phases in three types of planar lattices and the resulting mechanical properties of the two-dimensional networks. By creating a mapping from the space of design parameters to the space of mechanical properties, we are able to reduce the computational time required for evaluating each design to ≈2.4 × 10⁻⁶ s, and to make the process of evaluating different designs highly parallelizable. We then select ten designs to be 3D printed, mechanically test them, and characterize their behavior using digital image correlation to validate the accuracy of our computational models. Our simulation results show that our deep learning-based algorithms can accurately predict the mechanical behavior of the different designs and that our modeling results match experimental observations.

The reconstruction of large mandibular defects with optimal aesthetic and functional outcomes remains a major challenge for maxillofacial surgeons. The aim of this study was to design patient-specific mandibular reconstruction implants through a semi-automated digital workflow and to assess the effects of topology optimization on the biomechanical performance of the designed implants. By using the proposed workflow, a fully porous implant (LA-implant) and a topology-optimized implant (TO-implant) both made of Ti-6Al-4V ELI were designed and additively manufactured using selective laser melting. The mechanical performance of the implants was predicted by performing finite element analysis (FEA) and was experimentally assessed by conducting quasi-static and cyclic biomechanical tests. Digital image correlation (DIC) was used to validate the FE model by comparing the principal strains predicted by the FEM model with the measured distribution of the same type of strain. The numerical predictions were in good agreement with the DIC measurements and the predicted locations of specimen failure matched the actual ones. No statistically significant differences (p < 0.05) in the mean stiffness, mean ultimate load, or mean ultimate displacement were detected between the LA- and TO-implant groups. No implant failures were observed during quasi-static or cyclic testing under masticatory loads that were substantially higher (>1000 N) than the average maximum biting force of healthy individuals. Given its relatively lower weight (16.5%), higher porosity (17.4%), and much shorter design time (633.3%), the LA-implant is preferred for clinical application. This study clearly demonstrates the capability of the proposed workflow to develop patient-specific implants with high precision and superior mechanical performance, which will greatly facilitate cost- and time-effective pre-surgical planning and is expected to improve the surgical outcome.

Natural materials, such as nacre and silk, exhibit both high strength and toughness due to their hierarchical structures highly organized at the nano-, micro-, and macroscales. Bacterial cellulose (BC) presents a hierarchical fibril structure at the nanoscale. At the microscale, however, BC nanofibers are distributed randomly. Here, BC self-Assembles into a highly organized spiral honeycomb microstructure giving rise to a high tensile strength (315 MPa) and a high toughness value (17.8 MJ m-3), with pull-out and de-spiral morphologies observed during failure. Both experiments and finite-element simulations indicate improved mechanical properties resulting from the honeycomb structure. The mild fabrication process consists of an in situ fermentation step utilizing poly(vinyl alcohol), followed by a post-Treatment including freezing-Thawing and boiling. This simple self-Assembly production process is highly scalable, does not require any toxic chemicals, and enables the fabrication of light, strong, and tough hierarchical composite materials with tunable shape and size.

Non-affine deformations enable mechanical metamaterials to achieve their unusual properties while imposing implications for their structural integrity. The presence of multiple phases with different mechanical properties results in additional non-affinity of the deformations, a phenomenon that has never been studied before in the area of extremal mechanical metamaterials. Here, we studied the degree of non-affinity, Γ , resulting from the random substitution of a fraction of the struts,ρ_h, that make up a lattice structure and are printed using a soft material (elastic modulus = E_s) by those printed using a hard material (E_h). Depending on the unit cell angle (i.e., θ = 60°, 90°, or 120°), the lattice structures exhibited negative, near-zero, or positive values of the Poisson’s ratio, respectively. We found that the auxetic structures exhibit the highest levels of non-affinity, followed by the structures with positive and near-zero values of the Poisson’s ratio. We also observed an increase in Γ with EhEs and ρ_h until EhEs =10⁴ and ρ_h= 75%-90% after which Γ saturated. The dependency of Γ upon ρ_h was therefore found to be highly asymmetric. The positive and negative values of the Poisson’s ratio were strongly correlated with Γ. Interestingly, achieving extremely high or extremely low values of the Poisson’s ratio required highly affine deformations. In conclusion, our results clearly show the importance of considering non-affinity when trying to achieve a specific set of mechanical properties and underscore the structural integrity implications in multi-material mechanical metamaterials.

The emergence of advanced 3D printing techniques and the recent interest in architected materials have sparked a surge of interest in mechanical metamaterials whose unusual properties are defined by their highly ordered microarchitectures. Mechanical metamaterials with disordered microarchitectures have, however, not received as much attention despite their inherent advantages, such as robustness against the precise arrangement and design parameters of individual unit cells. Here, we computationally studied the elastic properties of two general types of disordered networks, namely, lattice-restricted and unrestricted networks that were made of beamlike elements and possessed mean connectivity values, Z, ranging between 2.5 and 7. We also additively manufactured a number of representative networks using selective laser sintering and showed that their deformations are consistent with our computational predictions. Unrestricted networks exhibited several advantages over the lattice-restricted ones including a broader range of achievable elastic modulus-Poisson's ratio duos as well as a higher probability of exhibiting auxetic and double-auxetic (i.e., auxetic behavior in both orthogonal directions) behaviors. Most interestingly, we could find unrestricted auxetic networks for high connectivity levels of up to 4.5, while no lattice-restricted auxetic networks were found for any connectivity level beyond 3.5. Given the fact that, according to Maxwell's criterion, 3.5 is the highest Z for which both of our lattice-restricted and unrestricted networks are bending-dominated, we concluded that unrestricted networks exhibit auxetic behavior well into their stretch-dominated domain. This is a promising observation that underlines the potential of unrestricted networks for the challenging task of designing stiff auxetic metamaterials in the stretch-dominated domain (i.e., Z = 4-4.5).

Up until recently, the rational design of mechanical metamaterials has usually involved devising geometrical arrangements of micro-architectures that deliver unusual properties on the macro-scale. A less explored route to rational design is spatially distributing materials with different properties within lattice structures to achieve the desired mechanical properties. Here, we used computational models and advanced multi-material 3D printing techniques to rationally design and additively manufacture multi-material cellular solids for which the elastic modulus and Poisson's ratio could be independently tailored in different (anisotropic) directions. The random assignment of a hard phase to originally soft cellular structures with an auxetic, zero Poisson's ratio, and conventional designs allowed us to cover broad regions of the elastic modulus-Poisson's ratio plane. Patterned designs of the hard phase were also used and were found to be effective in the independent tuning of the elastic properties. Close inspection of the strain distributions associated with the different types of material distributions suggests that locally deflected patterns of deformation flow and strain localizations are the main underlying mechanisms driving the above-mentioned adjustments in the mechanical properties.