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    ABSTRACT: Materials and microstructures with specific configurations are able to have negative Poisson’s ratio. This paper proposes a topology optimization methodology of frame structures to design a planar periodic structure that exhibits negative Poisson’s ratio. Provided that beam section of each existing member is chosen from a set of some given candidates, we can reduce the topology optimization problem to a mixed-integer linear programming problem. Since the proposed approach treats frame structures and stress constraints are rigorously addressed, the optimal solution contains no hinge region. A heuristic method with local search is used to solve large-scale problems. Numerical examples and fabrication test demonstrate that planar periodic frame structures exhibiting negative Poisson’s ratio can be successfully obtained by the proposed method.
    Optimization and Engineering 09/2013; · 0.83 Impact Factor
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    ABSTRACT: Metamaterials are rationally designed man-made structures composed of functional building blocks that are densely packed into an effective (crystalline) material. While metamaterials are mostly associated with negative refractive indices and invisibility cloaking in electromagnetism or optics, the deceptively simple metamaterial concept also applies to rather different areas such as thermodynamics, classical mechanics (including elastostatics, acoustics, fluid dynamics and elastodynamics), and, in principle, also to quantum mechanics. We review the basic concepts, analogies and differences to electromagnetism, and give an overview on the current state of the art regarding theory and experiment-all from the viewpoint of an experimentalist. This review includes homogeneous metamaterials as well as intentionally inhomogeneous metamaterial architectures designed by coordinate-transformation-based approaches analogous to transformation optics. Examples are laminates, transient thermal cloaks, thermal concentrators and inverters, 'space-coiling' metamaterials, anisotropic acoustic metamaterials, acoustic free-space and carpet cloaks, cloaks for gravitational surface waves, auxetic mechanical metamaterials, pentamode metamaterials ('meta-liquids'), mechanical metamaterials with negative dynamic mass density, negative dynamic bulk modulus, or negative phase velocity, seismic metamaterials, cloaks for flexural waves in thin plates and three-dimensional elastostatic cloaks.
    Reports on Progress in Physics 11/2013; 76(12):126501. · 13.23 Impact Factor
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    ABSTRACT: Auxetic behavior in low porosity metallic structures is demonstrated via a simple system of orthogonal elliptical voids. In this minimal 2D system, the Poisson's ratio can be effectively controlled by changing the aspect ratio of the voids. In this way, large negative values of Poisson's ratio can be achieved, indicating an effective strategy for designing auxetic structures with desired porosity.
    Advanced Materials 12/2013; · 14.83 Impact Factor