Thermodynamically consistent time-stepping algorithms for non-linear thermomechanical systems

We present the basic theory for developing novel monolithic and staggered time‐stepping algorithms for general non‐linear, coupled, thermomechanical problems. The proposed methods are thermodynamically consistent in the sense that their solutions rigorously comply with the two laws of thermodynamics...

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Bibliographic Details
Published in:International journal for numerical methods in engineering Vol. 79; no. 6; pp. 706 - 732
Main Author: Romero, Ignacio
Format: Journal Article
Language:English
Published: Chichester, UK John Wiley & Sons, Ltd 06.08.2009
Wiley
Subjects:
Algorithms
coupled problems
Entropy
Evolution
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
geometric integration
Mathematical analysis
Mathematical models
Nonlinearity
Physics
Preserves
Solid dynamics (ballistics, collision, multibody system, stabilization...)
Solid mechanics
Statistical physics, thermodynamics, and nonlinear dynamical systems
Structural and continuum mechanics
structure preservation
Symmetry
Thermodynamics
time integration
Invariant
coupled problems
Degenerate system
Displacement(deformation)
Evolution equation
Entropy
Isolated system
Dynamical system
Modeling
geometric integration
Thermodynamics
Coupled thermoelasticity
Pendulum
Numerical stability
Non equilibrium system
Step method
Thermomechanical properties
structure preservation
Non linear system
thermo- dynamics
Hamiltonian mechanics
Numerical simulation
Non linear effect
Hamiltonian
Time integration
ISSN:0029-5981, 1097-0207
Online Access:Get full text
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Summary:We present the basic theory for developing novel monolithic and staggered time‐stepping algorithms for general non‐linear, coupled, thermomechanical problems. The proposed methods are thermodynamically consistent in the sense that their solutions rigorously comply with the two laws of thermodynamics: for isolated systems they preserve the total energy and the entropy never decreases. Furthermore, if the governing equations of the problem have symmetries, the proposed integrators preserve them too. The formulation of such methods is based on two ideas: expressing the evolution equation in the so‐called General Equations for Non‐Equilibrium Reversible Irreversible Coupling format and enforcing from their inception certain directionality and degeneracy conditions on the discrete vector fields. The new methods can be considered as an extension of the energy–momentum integration algorithms to coupled thermomechanical problems, to which they reduce in the purely Hamiltonian case. In the article, the new ideas are applied to a simple coupled problem: a double thermoelastic pendulum with symmetry. Numerical simulations verify the qualitative features of the proposed methods and illustrate their excellent numerical stability, which stems precisely from their ability to preserve the structure of the evolution equations they discretize. Copyright © 2009 John Wiley & Sons, Ltd.
Bibliography:istex:FB7AA38F4E02C4412BAA02ADFCC522DF1AA62A5D
ark:/67375/WNG-XNJM0XXH-4
ArticleID:NME2588
Spanish Ministry of Education and Science - No. DPI2006-14104
ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0029-5981
1097-0207
DOI:10.1002/nme.2588