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This research focuses on improving the mechanical properties of auxetic mechanical metamaterials by various approaches, including structural reinforcement; introduction of novel deformation mechanisms; and integration of biomimetic structures to enhance stiffness, reduce buckling effects, and increase energy absorption capabilities in newly designed auxetic structures. In the results section, Chapter 3 presents a novel structural design based on a reentrant honeycomb to address the buckling issue in auxetic metamaterials, aiming to minimize the trade-off between auxetic behavior and stiffness. The innovative design includes a reinforced structure and a bimaterials approach with a tunable Young’s modulus in the soft hinges. The results indicated that stiffness increased by up to 133% (from 39 to 91 KPa) with the reinforced honeycomb structure compared to the conventional honeycomb structure, with minimal impact on auxeticity, which decreased by 46% (from -1.79 to -0.96) and strain -0.2%. Moreover, simulation results showed that the bimaterials approach efficiently controlled buckling, as peak stress concentration decreased from 50 to 0.6 MPa. This approach enhances the performance of the reentrant honeycomb structure, thus mitigating its impact on auxetic performance and producing stable, superior mechanical properties under uniaxial compression loads.Chapter 4 explores the development of a new auxetic metamaterial with a mechanically driven sliding mechanism, featuring a hexagonal profile for enhanced mechanical properties. Experimental and simulation results indicate that this unique design generates stable auxetic behavior without involving the bending-dominant mode commonly used in auxetic metamaterials. Along with the maintenance of stable auxetic behavior, the mechanical performance of this novel structure is shown to be four times stronger than that of conventional auxetic metamaterials, with a force response of 8000 N compared to 2000 N at a 50% strain in conventional materials. The simulation results also confirm the effectiveness of the newly proposed structure under different friction coefficients applied to the sliding interface. The results suggest that friction does not significantly affect auxetic behavior (~10%) but can potentially influence mechanical properties, with a 90% difference in terms of force response when the friction coefficient rises from 0.1 to 0.5 but starts to decrease when the coefficient reaches 0.7.Finally, Chapter 5 describes the innovative integration of mechanism-driven approaches into the design of bioinspired nacre structures to enhance stiffness, introduce auxetic behavior, and increase energy absorption capabilities under severe loading conditions. The results indicate that the introduction of auxeticity is beneficial for the nacre structure, with specific energy absorption increasing by 90%, from 2.50 to 4.75 J/g, under quasistatic compression loading and by 67% under low-speed impact loading compared to the nacre structure without auxeticity. Different impact-loading cases and the influence of detailed design parameters are also studied in Chapter 5. The results show that samples with 5% interconnection density and a 15° inclination angle have better mechanical performance compared to other combinations. In summary, this research proposes three innovative auxetic structures with the potential to advance the development in the field of metamaterials and biomimetic structures.

Coextrusion is shown to be a viable processing route for the fabrication of bioinspired ceramic materials that exhibit improved damage tolerance. This provides one of the few examples of the synthesis of "nacre-like" ceramic hybrid structures with “brick-and-mortar” architectures using a method that includes a metallic “mortar” (i.e., the compliant phase) during the entire fabrication process, instead of infiltrating it into a pre-fabricated ceramic scaffold. Detailed examination shows how manipulation of such processing can lead to improved mechanical performance in the resulting biomimetic ceramics by obtaining a model high volume fraction (~90 vol. %) ceramic with a brick-and-mortar architecture containing a metallic compliant phase. Specifically, brick-and-mortar alumina hybrid structures were synthesized containing small volume fractions (

Heterogeneous materials may become structurally unstable under an applied stress. In this thesis, the effects of two dissimilar stresses are studied. First, the methods of statistical mechanics are used to analyze the effects of mechanical stress on the strength of heterogeneous materials. A phenomenological multi-scale model is presented that analyzes inelastic deformation in a model natural composite, nacre. A kinetic Monte Carlo technique is developed to study the mechanical response of the biopolymer. The results of this model are used to generate a cellular automata model of the composite material. Under certain conditions, the sizes of plastic events in this model follow an apparent power-law distribution. The dynamics are found to be similar to earthquakes, where the slip sizes exhibit a scale-free distribution. Second, a continuum theory is generated to understand how a model microstructure responds to thermal stresses. At elevated temperatures, a structure may spontaneously change shape in order to minimize its overall surface energy. To this end, the stability of a hollow-core dislocation to pearling and coarsening is considered using a linear stability analysis. There is a competition between elastic energy and the anisotropic surface energy. It is shown that sufficiently small hollow-core dislocations are stable with respect to both forms of structural instability, suggesting a route to stabilize nanometer-scale wires.