Topological Design of Lattice Metamaterials with Unusual Mechanical Properties
- Publication Type:
- Thesis
- Issue Date:
- 2023
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Lattice metamaterials are artificially engineered materials that are composed of periodic cellular microstructures. They possess unusual physical properties that are not commonly observable in nature. Lattice metamaterials with exceptional mechanical properties have a variety of applications in aerospace, mechanical, vehicle, civil, and biomedical engineering. However, the current trial-and-error design method based on the intuition and experience cannot explore their full potential. New systematic design methods and novel metamaterials with unprecedented properties are in great demand.
Therefore, this research focuses on developing new systematic and rational design methods for finding lattice metamaterials with unusual mechanical properties. Novel microstructures that are found by the developed design methods would be studied and introduced in this research.
Firstly, this research developed a discrete topology optimization method for designing pentamode metamaterials with at least elastic orthotropic symmetry. Since a large ratio of bulk modulus to shear modulus is no more a sufficient condition for non-isotropic pentamode metamaterials, a new mathematical optimization formulation for finding such a material is established. Novel isotropic, transverse isotropic, and orthotropic pentamode microstructures have been found by the proposed design method.
Secondly, this research proposed a discrete topology optimization method for designing three-dimensional metamaterials with ideal elastic isotropy and extreme negative Poisson’s ratio, which are a type of unimode metamaterials. Novel three-dimensional strut-based isotropic unimode microstructures have been found, which are also capable of exhibiting tunable negative Poisson’s ratios by only altering their volume fractions.
Thirdly, this research developed a multi-material continuum topology optimization method for designing isotropic auxetic metamaterials with zero thermal expansion. The density clustering is used to guarantee that all intermediate designs during the optimization iterations have at least elastic cubic symmetry. A novel composite microstructure is numerically studied through finite element analyses to demonstrate its elastic isotropy, auxeticity, and thermal dimensional stability.
Finally, this research developed a multi-material discrete topology optimization method for designing isotropic lattice metamaterials with tunable thermal expansion and tunable auxeticity. Effective thermoelastic properties of potential designs described by a bi-material ground structure are calculated by using the computational homogenization method with beam elements. Novel strut-based composite microstructures are found and studied. By tailoring either the cross-sectional radii or the constituent material combination of struts, these microstructures can simultaneously exhibit elastic isotropy, tunable thermal expansion, and tunable auxeticity.
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