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Thermodynamics of Materials with Memory - Theory and Applications (Hardcover, 2nd ed. 2021)
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Thermodynamics of Materials with Memory - Theory and Applications (Hardcover, 2nd ed. 2021)
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This monograph deals with the mechanics and thermodynamics of
materials with memory, including properties of the dynamical
equations that describe their evolution in time under varying
loads. A work in four parts, the first is an introduction to
continuum mechanics, including classical fluid mechanics, linear
and non-linear elasticity. The second part considers continuum
thermodynamics and its use to derive constitutive equations of
materials with memory, including viscoelastic solids, fluids, heat
conductors and some examples of non-simple materials. In the third
part, free energies for materials with linear memory constitutive
relations are discussed. The concept of a minimal state is
introduced. Explicit formulae are presented for the minimum and
related free energies. The final part deals with existence,
uniqueness, and stability results for the integrodifferential
equations describing the dynamical evolution of viscoelastic
materials, including a new approach based on minimal states rather
than histories. There are also chapters on the controllability of
thermoelastic systems with memory, the Saint-Venant problem for
viscoelastic materials and on the theory of inverse problems. The
second edition includes a new chapter on thermoelectromagnetism as
well as recent findings on minimal states and free energies. It
considers the case of minimum free energies for non-simple
materials and dielectrics, together with an introduction to
fractional derivative models.
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