Modelling the deformation mechanisms, structure–property relationships and applications of auxetic nanomaterials

Analytical and Molecular Mechanics methods have been used to study the structure and deformation mechanisms acting at the molecular level in the auxetic polymorph of crystalline silica (α‐cristobalite). The Molecular Mechanics simulations indicate a stress‐induced phase transition from α‐cristobalite to ‘ordered’ β‐cristobalite occurs for uniaxial loading along the x 3 direction. This is in reasonable agreement with the previous prediction from an analytical model assuming deformation is by concurrent dilation and cooperative rotation (about axes in the x 1 ‐ x 2 plane, passing through the midpoints of opposing edges – the a ‐axes) of the SiO 4 tetrahedral molecular sub‐units, previously shown to predict the Poisson's ratio for loading in the x 3 direction. The analytical models have been extended to include cooperative rotation of each tetrahedron about its axis (the c ‐axis) mostly closely aligned with the principal unit‐cell x 3 ‐axis. The new models enable significantly improved prediction of the Poisson's ratios of α‐cristobalite when loaded in one of the transverse ( x 1 or x 2 ) directions. Parametric fitting of the analytical models indicate that the deformation mechanism for transverse uniaxial loading of α‐cristobalite is by concurrent dilation and cooperative rotation about the local a and c ‐axes of the SiO 4 tetrahedra. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)