An Introduction to the Phenomenological Theory of by J. Grindlay

By J. Grindlay

''In this monograph the writer describes the foundation and derivation of the macroscopic or phenomenological idea of the elastic, dielectric and thermal houses of crystals as utilized within the box of ferroelectricity. many of the effects and concepts defined are scattered in the course of the literature of this topic and this ebook offers them including their actual history in a single reference. The dialogue is specific to the speculation required to explain the houses of homogeneous specimens topic to low frequency fields.'' obtained it?

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Example text

C, V and A are the regions occupied in some arbitrary state by the conductor, dielectric and free space respectively (full lines). in the initial state be denoted by Fo, Co and AQ respectively and the corresponding regions in any other state by F, C and A (Fig. 2 . 5 . 1 ) . In the linear theory we are concerned only with small deformations of the dielectric and conductor relative to their configurations in the initial state and hence F ~ Fo and C ~ Co. Extending the notation introduced in § 2 .

2 . 3 . 9 ) and ( 2 . 3 . 1 0 ) ] , dv (/ = 1, 2 , 3 ) , (/ = 1, 2 , 3 ) , υ since Tj¡ is symmetric. It is clear from these two expressions that we can fully represent the effect of the stress tensor in both F and Γ" by a body force of d e n s i t y ^ 67},/9x,. Conversely, if we obtain a symmetric j OX"' tensor Tj¡ such that / / = X -^-^ (and this can always be done for any arbitrary vector), then we can fully represent the effect of the body force by a stress field T^rij, These results suggest that it is redundant to introduce two fields / and / a s we have done in § 2 .

However, if additional fields are required to describe the net force on v, the field equations derived from the conservation of linear momentum and the conservation of angular momentum may not yield such a simple solution (Truesdell and Toupin, 1 9 6 0 . 4 BOUNDARY CONDITIONS The arguments in § 2 . 3 . 3 , which led to the introduction of the stress tensor, also yield the conditions to be satisfied by the stress tensor field at the boundary of the body. Suppose the body is subjected to surface tractions represented by the stress field t^.

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