By Birkhoff G.D.
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Extra info for A Theory of Matter and Electricity
In particular, the stressstrain and electric field-electric displacement relations are linear if the stresses and field strengths are sufficiently small that the domain reorientation processes be reversible. In this case the constitutive equations of x 3-polarized piezoceramic are the same as for a piezocrystal of the hexagonal 6mm symmetry class (with the symmetry axis colinear with x 3), and its mechanical, dielectric and piezoelectric properties are determined by five elasticity moduli (or compliances), two dielectric permittivities and three piezoelectric constants.
It should be understood, however, that the (initial) domain orientation pattern is intrinsically random and as such need not secure the energy minimum. Rather, the material will be in what is known as a metastable state, and its domain structure will change not only under the action of thermal, electric or mechanical fields, but also in the absence of any external influence (which is ageing). It has been pointed out by Tarasova et al.  that apart from domains, such polar elements as domain wedges or charged point defects may violate the equilibrium state of a piezoceramic.
12 where pis the mass density. 37). 48) 0 where s~icT are the isothermal elastic compliances, drii are the piezoelectric moduli, Eij' T the dielectric permittivities, P; the pyroelectric coefficients, cu,E the specific heat at constant stress and electric field, and the coefficients of thermal expansion. 14) if Ei = 0. In solving specific problems it is convenient - and customary - to introduce a system of abbreviated subscripts for material parameters. Since the stress and strain tensors are symmetric, each component can be specified by one subscript rather than two.