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Title: Variational integrators for the dynamics of thermo-elastic solids with finite speed thermal waves

This paper formulates variational integrators for finite element discretizations of deformable bodies with heat conduction in the form of finite speed thermal waves. The cornerstone of the construction consists in taking advantage of the fact that the Green–Naghdi theory of type II for thermo-elastic solids has a Hamiltonian structure. Thus, standard techniques to construct variational integrators can be applied to finite element discretizations of the problem. The resulting discrete-in-time trajectories are then consistent with the laws of thermodynamics for these systems: for an isolated system, they exactly conserve the total entropy, and nearly exactly conserve the total energy over exponentially long periods of time. Moreover, linear and angular momenta are also exactly conserved whenever the exact system does. For definiteness, we construct an explicit second-order accurate algorithm for affine tetrahedral elements in two and three dimensions, and demonstrate its performance with numerical examples.
Authors:
 [1] ;  [2] ;  [1]
  1. Department of Mechanical Engineering, Stanford University, Stanford, CA 94305-4040 (United States)
  2. (CIEP), Conicyt Regional/CIEP R10C1003, Universidad Austral de Chile, Ignacio Serrrano 509, Coyhaique (Chile)
Publication Date:
OSTI Identifier:
22230856
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 257; Journal Issue: Part B; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ALGORITHMS; ANGULAR MOMENTUM; CONSTRUCTION; ELASTICITY; ENTROPY; FINITE ELEMENT METHOD; GEOMETRY; HAMILTONIANS; SOLIDS; THERMAL CONDUCTION; VARIATIONAL METHODS