Minimal states and maximum free energies of materials with memory |
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Affiliation: | 1. Institute of Thermomechanics, Dolejskova 5, Prague 8, 182 00, Czech Republic;2. School of Engineering, Heriot-Watt University, Edinburgh EH14 4AS, UK;3. IDMEC - Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal |
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Abstract: | Definitions are given of the maximum and minimum free energy associated with a given state of a material with memory. Also, the concept of a minimal state is introduced. These concepts are then explored in detail for a specific isothermal model, where the stress is given by a non-linear elastic part and a memory part which is a linear functional of the strain tensor history. It is shown that the equivalence class constituting a minimal state is a singleton except where only isolated singularities occur in the Fourier transform of the relaxation tensor derivative. If the minimal state is not a singleton, then the maximum free energy is less than the work function and is a function of the minimal state. An explicit expression is given for the maximum free energy. |
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