Free energies for materials with memory in terms of state functionals. (English) Zbl 1299.74010
Summary: The aim of this work is to determine what free energy functionals are expressible as quadratic forms of the state functional \(I^t\) which is discussed in earlier papers. The single integral form is shown to include the functional \(\psi _F\) proposed a few years ago, and also a further category of functionals which are easily described but more complicated to construct. These latter examples exist only for certain types of materials. The double integral case is examined in detail, against the background of a new systematic approach developed recently for double integral quadratic forms in terms of strain history, which was used to uncover new free energy functionals. However, while, in principle, the same method should apply to free energies which can be given by quadratic forms in terms of \(I^t\), it emerges that this requirement is very restrictive; indeed, only the minimum free energy can be expressed in such a manner.
MSC:
| 74A15 | Thermodynamics in solid mechanics |
| 74D99 | Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) |
| 74G65 | Energy minimization in equilibrium problems in solid mechanics |
Keywords:
thermodynamics; memory effects; free energy functional; minimal state functional; rate of dissipationReferences:
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