Multiscale Hybrid Materials with Negative Poisson’s Ratio
Negative Poisson’s ratio, while thermodynamically permitted, is only observed in some natural crystals in certain directions. All other known cases of negative Poisson’s ratio are the man-made structures which exhibit this property macroscopically. One class of these structures includes re-entrant foams and special structures with springs and hinges. Another class is constituted by materials consisting of a matrix with positive Poisson’s ratio with embedded microstructural elements producing macroscopic negative Poisson’s ratio. In the first class, we propose structures made of balls bonded by links with high shear to normal stiffness ratio. In the second class, we introduce materials filled with cracks with suppressed relative shearing of the faces. In the latter case we determine the effective moduli for multiscale crack distributions using the differential self-consistent method and show that the minimum value of Poisson’s ratio achievable in this way is −1/3. Materials with positive and negative Poisson’s ratio can be combined into hybrid materials. For multiscale distribution of inclusions (wide distribution of sizes with the same concentration at each scale) we show that negative Poisson’s ratio spherical inclusions in a positive Poisson’s ratio elastic isotropic matrix considerably increase the effective Young’s modulus even when the Young’s moduli of the matrix and inclusions are the same.
KeywordsHomogenisation multiscale distribution inclusions with negative Poisson’s ratio differential self-consisted method
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