Energy–entropy–momentum integration schemes for general discrete non‐smooth dissipative problems in thermomechanics. (21st March 2017)

• Record Type: Journal Article
• Authors: Portillo, D.; García Orden, J. C.; Romero, I.
• Is Part Of: International journal for numerical methods in engineering. Volume 112:Number 7(2017)
• Page Start: 776
• Page End: 802
• Publication Date: 2017-03-21
• Subjects: time integration -- thermo‐elasto‐plasticity -- structure preserving integration, coupled problems -- metriplectic systems; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5532
• Languages: English
• ISSNs: 0029-5981

Abstract

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.