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Energy–entropy–momentum integration schemes for general discrete non‐smooth dissipative problems in thermomechanics
Author(s) -
Portillo D.,
García Orden J. C.,
Romero I.
Publication year - 2017
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5532
Subject(s) - discretization , dissipative system , nonlinear system , integrator , mathematics , entropy (arrow of time) , hardening (computing) , computer science , mathematical analysis , physics , thermodynamics , materials science , computer network , bandwidth (computing) , layer (electronics) , quantum mechanics , composite material
Summary We present the theory of novel time‐stepping algorithms for general nonlinear, non‐smooth, coupled, and 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. Extending previous works on the subject, the newly proposed integrators are applicable to coupled mechanical systems with non‐smooth kinetics and can be formulated in arbitrary variables. The ideas are illustrated with a simple non‐smooth problem: a rheological model for a thermo‐elasto‐plastic material with hardening. 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 © 2017 John Wiley & Sons, Ltd.