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Free energy and states of fractional-order hereditariness |
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| Authors: | Luca Deseri Mario Di Paola Massimiliano Zingales |
| Institution: | 1. Dipartimento di Ingegneria Civile, Ambientale e Meccanica, Via Mesiano n.77, 38123 Trento, Italy;2. Dept. of Civil Environmental Engineering, Carneige-Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213-3890, USA;3. TMHRI-Department of Nanomedicine, The Methodist Hospital Research Institute, 6565 Fannin St. MS B-490, Houston, TX 77030, USA;4. Dipartimento di Ingegneria Civile, Ambientale, Aerospaziale, dei Materiali, Viale delle Scienze Ed.8, 90128 Palermo, Italy;5. Laboratory of Bio-NanoMechanics in Medicine (BNM2-LAB), Mediterranean Center of Human Health and Advanced Biotechnologies, Viale delle Scienze Ed.18, 90128 Palermo, Italy |
| Abstract: | Complex materials, often encountered in recent engineering and material sciences applications, show no complete separations between solid and fluid phases. This aspect is reflected in the continuous relaxation time spectra recorded in cyclic load tests. As a consequence the material free energy cannot be defined in a unique manner yielding a significative lack of knowledge of the maximum recoverable work that can extracted from the material. The non-uniqueness of the free energy function is removed in the paper for power-laws relaxation/creep function by using a recently proposed mechanical analogue to fractional-order hereditariness. |
| Keywords: | Fractional derivatives Power-law creep/relaxation Free energy Dissipation rate Material state |
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