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Can a Linear Anisotropic Elastic Material Have a Uniform Contraction under a Uniform Pressure?

University ofIllinois at Chicago, 842 West Taylor Street (M/C 246), Chicago, IL 60607-7023, USA

When a linear isotropic elastic material is under a uniform pressure, it produces a uniform contraction. If the material is anisotropic, it in general does not produce a uniform contraction except for a cubic material. We will show that there are special linear anisotropic elastic materials other than cubic materials for which a uniform contraction is possible under a uniform pressure. The material can be any one of the eight crystal groups. It means that the material can be monoclinic, orthotropic, trigonal, tetragonal, transversely isotropic, and, of course, cubic or isotropic. It can also be triclinic; that is, the material need not possess a plane of symmetry.

Key Words: anisotropy • elasticity • uniform contraction • uniform pressure • material symmetry

Mathematics and Mechanics of Solids, Vol. 6, No. 3, 235-243 (2001)
DOI: 10.1177/108128650100600301


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