Constitutive equations for transversely isotropic elastic dielectrics with Schur's lemma

Group-theoretic methods are used to impose symmetry restrictions on the form of the constitutive equations of linear theory of elastic dielectrics. A particular case of transversely isotropic elastic dielectrics which belong to the D-6(622) crystal class and are governed by a group of 12 symmetry transformations and 6 irreducible representations associated with each element is discussed in detail. The product table is constructed and used to derive the basic quantities associated with the irreducible representations. Schur's lemma is applied to the constitutive equations and non-vanishing constants are determined from the linear algebraic systems and presented in tables. The number of independent material constants is reduced from 171 to 25. (C) 2001 Elsevier Science Ltd. All rights reserved.