A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids
By Qiang Yang, Laurent Stainier, Magdalena Ortiz. 2006
249 citations recorded by the source corpus.
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.
Subfields: Biomedical Engineering, Materials Chemistry, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/297eb94c7c564929732eb6e39d0130272513cf27
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Citations in the corpus
- Towards variational constitutive updates for non-associative plasticity models at finite strain: models based on a volumetric-deviatoric split (2009, background): “For instance, the extensions necessary to include temperature effects were discussed in [ 22 , 23].”
- An explicit discontinuous Galerkin method for non‐linear solid dynamics: Formulation, parallel implementation and scalability properties (2008, unknown): “This framework has recently been extended to the coupled thermomechanical response of general dissipative solids [17].”
- On the implementation of rate-independent standard dissipative solids at finite strain – Variational constitutive updates (2010, background): “More precisely, and in line with [19], an additional term depending on the rate of the inelastic strains has simply to be added to Eq. (20) in this ca se. Details about the non-trivial extensions required for viscoelasticity or thermomechanically coupled problems which are beyond the scope the prese”