Design, Modeling and Numerical Investigation of Multi-Scale Materials

Mechanical metamaterials are designed to provide desired behaviors for engineering and scientific researches using multi-scale modeling techniques. The proliferation of new technological facilities emphasize the advancements of engineering design and mechanical testing methodologies. As a matter of fact, these modeling techniques play an effective role in the investigation of complex of diverse materials, mechanical metamaterials. Renewed metamaterial types inspired by materials found in nature are becoming a popular concept. Therefore, additive manufacturing, namely 3D printing, is used to fabricate the complex microstructures and reveal internal structural pattern contribution. The layer-upon-layer approach in additive manufacturing, along with open or closed cells in polymeric or metallic foams, involves an intrinsic microstructure tailored to the underlying applications. With developed mathematical models, higher-order theories and approaches are utilized to identify extraordinary material responses by homogenizing such architectured materials. In fact, classical models and processes with high computational efficiency are being replaced by systematic frameworks based on new methods and principles, particularly when the microstructure’s characteristic length is comparable to the length scale of the structure. While classical homogenization approaches applied to heterogeneous materials are suitable for cases where scale separation is evident, they fail to be accurate when the effective continuum’s length scale approaches the characteristic length of the material’s microstructure. In such cases, highergradient theories can be employed to enable multi-scale material modeling of complex structures, both in terms of geometry and material properties. Therefore, second-order modeling in mechanics is used to study and determine the additional constitutive parameters that arise from strain-gradient theory