A remapping scheme for history‐dependent material state variables

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 classic...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2020-07, Vol.121 (14), p.3132-3158
Main Authors: Versino, Daniele, Mourad, Hashem M., Luscher, Darby J.
Format: Article
Language:English
Subjects:
advection
arbitrary eulerian lagrangian
Dependent variables
History variables
Interpolation
Optimization
remapping
State variable
state‐dependent variable
Transport equations
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Summary: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.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.6350