Rotation and dilation deformation mechanisms for auxetic behaviour in the α-cristobalite tetrahedral framework structure |
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| Authors: | A Alderson K E Evans |
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| Institution: | (1) BNFL, Research and Technology Building 709, Springfields, Preston PR4 0XJ, UK, GB;(2) Department of Engineering, University of Exeter, North Park Road, Exeter EX4 4QF, UK, GB |
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| Abstract: | Analytical expressions are derived for the Poisson's ratios associated with a three-dimensional network of regular, corner-sharing
tetrahedra in which: (1) the tetrahedra are assumed to be rigid and free to rotate relative to each other; (2) the tetrahedra
are assumed to maintain shape and orientation but are free to change size (dilate); (3) tetrahedral rotation and dilation
are assumed to act concurrently. The structure has a primitive unit cell containing four tetrahedra and is analogous to the
molecular structure of α-cristobalite. Strain-dependent variations in Poisson's ratio are also predicted by the models. For
deformation due to tetrahedral rotation the network is found to exhibit negative Poisson's ratios in each of the three principal
directions, with the magnitude of the Poisson's ratio being dependent on the angle of rotation of the tetrahedra. The behaviour
of the Poisson's ratio is isotropic in the transverse plane, but anisotropic elsewhere. In the dilation model negative Poisson's
ratios equal to −1 are observed for uniaxial loading in any of the principal directions, with the value being constant irrespective
of tetrahedral size. The model for concurrent tetrahedral rotation and dilation allows positive as well as negative Poisson's
ratios, with the values determined by the framework geometry and relative strengths of the two mechanisms. The concurrent
model also offers a design route to materials and structures having ultrahigh Young's moduli.
Received: 15 February 2000 / Accepted: 1 October 2000 |
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| Keywords: | Tetrahedral framework Negative Poisson's ratio Auxetic Elastic constants Silica |
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