A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids
A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids is presented. The coupled thermo-mechanical boundary-value problem under consideration consists of the equilibrium problem for a deformable, inelastic and dissipative solid with the heat conduction problem appended in addition. The variational formulation allows for general dissipative solids, including finite elastic and plastic deformations, non-Newtonian viscosity, rate sensitivity, arbitrary flow and hardening rules, as well as heat conduction. We show that a joint potential function exists such that both the conservation of energy and the balance of linear momentum equations follow as Euler–Lagrange equations. The identification of the joint potential requires a careful distinction between equilibrium and external temperatures, which are equal at equilibrium. The variational framework predicts the fraction of dissipated energy that is converted to heat. A comparison of this prediction and experimental data suggests that α-titanium and Al2024-T conform to the variational framework.
© 2005 Elsevier. Received 27 April 2005, Revised 13 August 2005, Accepted 22 August 2005, Available online 6 October 2005. We are grateful for support provided by Caltech's NSF/MRSEC Center for the Science and Engineering of Materials, and DARPA's Structural Amorphous Metals program through Caltech's Center for Structural Amorphous Metals. We also gratefully acknowledge the support of the Department of Energy through Caltech's ASCI/ASAP Center for Simulating the Dynamic Response of Materials. LS is Research Associate at the Fonds National de la Recherche Scientifique of Belgium.