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Extreme Lamé Compliance in Crystals of Trigonal Symmetry: the Case of -Quartz

Department of Mechanical Engineering, University of Houston, Houston, TX, USA

The variation of the Lamé compliance with direction is explored for elastic crystals associated with the trigonal class possessing six independent compliances (associated with point groups 32, 3m, 3m). A new decomposition of the compliance tensor is presented that simplifies the Lamé compliance by reducing the number of elastic parameters required to analyze how it varies with direction. The common form of quartz referred to as -quartz falls within this class and is known to possess such interesting elastic properties as negative Poisson ratios. The Lamé compliance is a convenient indicator of this negativity and furnishes a sharp connection between its extreme directions and the underlying lattice orientation of the material.

Key Words: Lamé compliance • Poisson's ratio • trigonal symmetry • operator decomposition

Mathematics and Mechanics of Solids, Vol. 14, No. 1-2, 135-147 (2009)
DOI: 10.1177/1081286508092607


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