Abstract
We now apply thermodynamic principles to field theories with memory. For general nonlinear, nonisothermal theories, we assume that a free energy is given, this being the fundamental constitutive assumption. Applying a generalization of the approach of Coleman [36], Coleman and Mizel [38], Gurtin and Pipkin [130], we derive the constitutive equations for the theory in Section 5.1. Also, fundamental properties of free energies are derived. Furthermore, some observations are made on the case of periodic histories and in relation to constraints on the nonuniqueness of free energies. In Section 5.2, an expression for the maximum recoverable work is given for general materials, together with an integral equation for the process yielding this maximum. Finally, in Section 5.3, we discuss how free energies can be constructed from combinations of simpler free energies.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Amendola, G., Fabrizio, M., Golden, J.M. (2012). Thermodynamics of Materials with Memory. In: Thermodynamics of Materials with Memory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1692-0_5
Download citation
DOI: https://doi.org/10.1007/978-1-4614-1692-0_5
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4614-1691-3
Online ISBN: 978-1-4614-1692-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)