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A remapping scheme for history‐dependent material state variables
Author(s) -
Versino Daniele,
Mourad Hashem M.,
Luscher Darby J.
Publication year - 2020
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.6350
Subject(s) - state variable , interpolation (computer graphics) , monotone polygon , mathematics , scheme (mathematics) , mathematical optimization , nonlinear system , state (computer science) , computer science , algorithm , mathematical analysis , geometry , animation , physics , computer graphics (images) , quantum mechanics , thermodynamics
Summary We present an interpolation scheme for use with material models involving history‐dependent state variables. The interpolation scheme is based on the solution of a constrained optimization problem, to identify the smoothest monotone curve which produces an admissible solution. Unlike classical schemes used for transport equations, the proposed methodology accounts for the interdependence of the history variables and produces admissible interpolations of the material's state variables. After introducing a general solution scheme for the problem, a simplified and more computationally efficient method is derived. Finally, as a validation problem for the proposed methods, we consider the advection of internal state variables belonging to material models with highly nonlinear yield surfaces.