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Abstract
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| We present the basic theory for developing novel monolithic and staggered time-stepping al- gorithms for general non-linear, non-smooth, coupled, thermomechanical problems. This work is an extension of the methods presented by Romero [1] to non-smooth 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. The formulation of such methods is based on two ideas: express- ing the evolution equation in the so-called General Equations for Non-Equilibrium Reversible Irreversible Coupling (GENERIC) and enforcing from their inception certain directionality and degeneracy conditions on the discrete vector fields. Initially employed for the description of smooth models, GENERIC was recently extended to encompass non-smooth kinetic processes by Mielke [2]. This extension is useful in solid mechanics, for example, in order to encompass plastic effects which are non-smooth by nature. In the presentation, the new ideas are applied to a simple coupled problem: a rheological model for a thermo-elasto-plastic material with hardening. Numerical simultions 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. | |
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International
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Si |
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Congress
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15th European Mechanics of Materials Conference |
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960 |
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Place
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Brussels |
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Reviewers
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Si |
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ISBN/ISSN
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000-00-0000-000-0 |
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Start Date
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07/09/2016 |
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End Date
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09/09/2016 |
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From page
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0 |
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To page
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1 |
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15th European Mechanics of Materials Conference |