Abstract
We now consider special cases of the constitutive relations (7.1.13), namely linear viscoelastic solids and fluids with linear memory under isothermal conditions in the present chapter and an approximate version of rigid heat conductors in Chap. 9. Some of the formulas are similar to those derived in the general case, and detailed proofs are omitted or a different version is given. Other formulas are specific to completely linear materials , for example.
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Notes
- 1.
The quantity I t was originally defined in the literature as the negative of the functional used here. This change in sign, which is consistent with Sect. 7.4, is introduced here and later so that its relationship with the stress functional is a little more precise.
- 2.
Note that the tensor \(\mathbb {K}\) here is quite different from the quantity used briefly in the early part of Sect. 7.1.
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Amendola, G., Fabrizio, M., Golden, J. (2021). Viscoelastic Solids and Fluids. In: Thermodynamics of Materials with Memory. Springer, Cham. https://doi.org/10.1007/978-3-030-80534-0_8
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