Biomedical Engineering Reference
In-Depth Information
3. A small change in stress produces a change in strain according to the equation:
d ε ij
= s ijkl d σ kl
(3.3)
where s ijkl are the elastic compliances.
Figures 3.1 and 3.2 also illustrate relations that are called coupled effects . These are
denoted by the lines joining pairs of points which are not both at the same corner.
In the two diagonal lines at the bottom of the diagram, one shows thermal expansion ,
the strain produced by a change in temperature, while the other shows the piezocaloric
effect , that is, the entropy (heat) produced by a stress. These coupled effects connect
scalars with second-rank tensors and are, therefore, themselves specified by second-rank
tensors. As an example, for thermal expansion, the relation is:
d ε ij
= α ij d T
(3.4)
Figure 3.1 The physical relationships between the mechanical, electrical, and thermal properties
of a crystal. The tensor rank of each variable is shown in round brackets and the rank of properties
in square brackets (By permission of Oxford University Press)
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